Generative composition with texture groups

ABSTRACT

A computer-implemented method of generating a musical composition containing a plurality of musical texture groups is disclosed. The method includes assembling musical texture groups from musical instrument components and associating therewith a tag expressing emotional textural connotation. The instrument components have musical textural classifiers selected from a set of pre-defined textural classifiers such that different instrument components may have a different subset of pre-defined textural classifiers. The textural classifiers within a texture group possess either no musical feature attribute or a single musical feature attribute and any number of musical accompaniment attributes. The method then generates at least one chord scheme to a narrative brief, to provide an emotional connotation to a series of events, the chord scheme generated by selecting and assembling Form Atoms. The final step includes applying a texture to the chord scheme to generate the musical composition reflecting the narrative brief.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of and claims priority toU.S. application Ser. No. 17/219,610 that was filed on Mar. 31, 2021 andwhich is fully incorporated herein by reference.

BACKGROUND TO THE INVENTION

This invention relates, in general, to signal processing by an apparatusof an audio input signal to split that signal into fundamentalconstituent data elements, and the mathematical functions thereofnecessary to reproduce this signal as well as a plethora of new signals,with differing internal structural properties and differing boundaryconditions that permit, through mapping and/or textural classification,the identification of both permissible linkages between constituent dataelements and subsequent generative output from the identifiedmathematical functions, concatenated re-assembly into a different signalwith a different structure. More particularly, the present inventionrelates to a system supporting original generative composition, not justrecombination of existing material especially in the context of musicand how an original composition can be generated to align with andreflect an emotionally descriptive narrative, such as a described scenein a film script. More particularly, but not exclusively, the presentinvention relates to a process for identifying and parsing, in existingtonal (as well as non-tonal) music, Form Atoms of varying length andwhere each Form Atom defines a contextually smallest meaningful snippetor element of musical content having both boundary conditions andcompositional properties that permit automated concatenation of multipleForm Atoms into a new musical composition having good musical form butat least acceptable musical form.

SUMMARY OF THE PRIOR ART

Music in its own right does not exist because it is undetectable byscience. Rather, music reflects observation by the mind that provides aresponse in the brain. A profound couple of statements but reflective ofthe fact that music and, more particularly, the appreciation of musicreduces to signal processing and mental stimulation associated with theinterpretation of a subjectively constructed journey in sound thatexploits the concepts of “tension” and “release” as each is resolved inthe mind of the listener. Regardless of what music amounts to andwhether it is based on western, tribal or oriental structures, there aredesirable physiological effects associated with music, with theseeffects further affecting emotional responsiveness and demeanour.

Music theory has traditionally been more of a folk psychology used toname and categorise music, rather than a theory in a scientific sensethat can predict the effectiveness of a passage, or the next note orchord in a piece.

‘Good’ music—in the sense of an artistically appreciated structuredcomposition—is music that the mind (i.e., relevant neural pathways andcentres of the brain) models successfully by being able to predict bothan increase in tension within a musical journey and then the followingrelease of that tension. Alternatively, this can be thought of as acompositional piece asking a question, as reflected in musical phrasingor musical structure, and then the compositional piece answering thatquestion shortly after the question has been posed to permit mindfultermination of a particular part within the entirety that is the musicaljourney in the composition. The question is thus a construct of tensionin the music, and the release of a construct that correlates to anappropriate musical answer that puts the change in tonality intoperspective. A more complete definition is provided below for theseterms to enhance the reader's understanding of what these semantic termsmean in a more technical sense.

Putting the above into a psychological perspective, “good music” isrecognised through a self-gratification process in which the mindfirstly predicts what it thinks will be delivered by the musicaljourney, and when an “I was right” prediction is confirmed the rewardsystem of the brain triggers to complete the reward. Whilst not wishingto be bound by theory, it is understood that the reward system refers toa group of structures that are activated by rewarding or reinforcingstimuli. When exposed to a rewarding stimulus (such as good music), thebrain responds by increasing the release of the neurotransmitterdopamine. The structures associated with the reward system are foundalong the major dopamine pathways in the brain, including the ventraltegmental area (VTA) and the nucleus accumbens in the ventral striatum.Another major dopamine pathway, the mesocortical pathway, travels fromthe VTA to the cerebral cortex and is also considered part of the rewardsystem.

In contrast, “bad music” or bad composition or “bad form” corresponds toreduced reward/gratification that arises from the brain's inability topredict anything from seemingly/ostensibly meaningless random musicalevents, and thus the brain's inability to congratulate itself with areward arising from stimulation.

A significant and unaddressed problem that has prevented the effectiveautomated generation of “good” music is “form”. The question is how toimplement technically a process that does not generate randomness andwhich technical system is imbued with a technical mechanism thatprovides consistent evaluation of signal components initially toclassify fundamentally compatible musical sections and then to permitthose musical sections to be automatically selected and concatenatedtogether seamlessly to provide a new generative composition; this is farfrom simple.

In fact, with respect to “form” composers require experience to identify“form”, and even accomplished composers frequently have failed toappreciate acceptable form until later in their evolutionarycompositional life. Even with the gained appreciation of form, composersfrequently revert to templates in all their compositions. Templatesprovide a pre-structured structure on which the desired narrative ishung. A template can, for example, be sonata form or a rondo and otherforms, as will be understood. As a specific example, the first movementof any symphony or concerto will share an identical form but a differentnarrative, e.g. A-B-A-B-C and then D, where A is the first subject inthe major/dominant tonic, B is a contrasting key centre to themajor/dominant tonic and A and B together form the “exposition”, C isthe conflict between A and B (which is also known as the “development”)and D is the “recapitulation” or resolution of A and B.

“Form”, in contrast with “narrative”, the latter being what one intendsto express musically, i.e., the story between a beginning and end pointas expressed by a set of emotional icons such as intensity swells andclimaxes, is the structure of linking musical elements together in amusically sensible fashion that avoids discontinuity or randomness (inmusical terms) such that a smooth transition is achieved between thesyntax of the composite elements. Expressing “form” more tangibly butstill subjectively, “good form” may be the syntax reflected in codes andconventions in accepted musical compositions, whereas “bad form” has noobvious or known linking that makes any discernible musical sensebetween successive musical elements/phrases and, indeed, “bad form” inmusic will fail to communicate structure because the sound signalscannot logically be processed by the brain.

The problem is that when any generative composition needs to adapt tofollow a narrative that is different than that that can be laid down byan initial form template, regardless of whether it is human ormachine-based, systems struggle to realise a generative mechanism thatconsistently achieves “good form” and thus the generation of relativelyhigh levels of dopamine in the brain's reward centres. And with afailure to achieve “good form”, by definition the composition acquires“bad form” and correspondingly identifiable qualitative and/ormeasurable decreases in brain stimulation, particularly associated withthe reward centres. Effective generative composition thus leads to atangible technical effect with an associated technical assessmentprocess. Indeed, better generative composition leads to increasinglevels of detectable stimulation/brain activity.

Indeed, identification of common musical traits in splice compatiblemusical elements is desirable and useful to game developers and/oradvert or film trailer producers/editors who are tasked with rapidlycompiling a suitable multimedia product that aligns relevant musicthemes, such as increasing musical intensity (in the context of anincreasing sense of developing drama and urgency and not necessarily inthe context of an absolute audio power output level) with video output.To provide a context for the problem of composition in a commercialenvironment, the generation of an appropriate film score is a firstexample. Currently, the film director will write a narrative reflectingthe evolution of action in a scene and will then approach a composer fora suitable composition. The composer will review the narrative andattempt to tailor a composition to the narrative in the provision of a“demo” to the client, such as a film director or game designer.

More particularly, music for films, TV and adverts follows a similarcommissioning and production pattern. A composer is commissionedtypically by a director or producers. Their choice of the composer iseither based on a musical showreel, or through the fact that thecommissioner knows the composer's specific discourse and desires it fortheir project. Before the composer views the pictures, a temp track istypically used to aid in the editing process as well as to give an ideafor the type of pace and mood that the commissioner wishes the film tohave at specific points. The composer and commissioner then meet forwhat is known as a “spotting session”. In this meeting, the parties viewthe temp track and discuss the project in terms of where the musicshould start and stop, a process known as spotting. All other parametersfor each section of self-contained music, or music cue, in the film arealso considered. This process completes the brief, which consists ofentry and exit timings for each cue, any hit points within the cue, andthe mood, orchestration, and pace of the cues. Hit points are points onthe timeline where the music should “hit” the action, such as Tom beinghit over the head with a frying pan by Jerry. From this, the composerproduces a demo of the desired tracks for each cue. These tracks arethen auditioned by the commissioners and feedback is provided for thecue's refinement. Once the tracks are considered to be in a satisfactorystate by all parties, they are then recorded, or baked as it is known.

Interestingly, film composers are prone to borrow and steal ideas fromhistorical pieces and those of other contemporary composers in order tosatisfy various briefs, just as John Williams did when lifting acomplete orchestral section of the closing of Mars from Holst's ThePlanets suit in his opening credits for the film Star Wars (Kurtz &Lucas, 1977). Indeed, this point is openly spoken about by John Williamshimself in an interview with David Meeker at the BFI (Meeker, 1978).Indeed, it is evidently clear that composers revisit scores and not onlytweak them as Bach did (Ledbetter, 2002), but completely reform them soas to make a better temporal narrative, as was the case withRachmaninoff s Piano Concerto No. 4 (Norris, 2001).

This also leads to the question of the presently perceived artisticprocess of composition, although with generative composition this mustnecessarily technically assess “form” and for such “form” to bemaintained sufficiently under the control of the system intelligenceassembling the generative work.

This iterative process of film score multimedia composition may—or maynot—lead to a composition that has “good form”, and it will involveagain the film director in making a decision as to whether the remotelycomposed score is acceptable with the requisite level of “good form”.The composer, as indicated above, is likely also to be influenced bytheir own prior compositions and, frequently, will make use of thesepersonal templates in composing the “new” musical work. The use of suchpersonal templates, which generally means that they have accepted formqualities, invariably leads to a score that is “samey”; this is notnecessarily a good thing. For example, there are noticeable commontraits in the compositions of the main themes for the movies Superman®and Star Wars® since both were penned by John Williams.

In providing at least one resultant “demo” for review, the developer oreditor has already expended considerable time in identifying potentiallysuitable music and then fitting/aligning the selected music to thevideo. To delay having to identify a commercially-usable audio track,content developers presently may make use of so-called “temp tracks”that are often well-known tracks having rights that cannot be easilyobtained, but this is just a stop-gap measure because a search is thenrequired to identify a suitable commercially-viable track for which userights can be obtained. Further time delays then arise from theinstructing client having to assess whether the edit fits with theiroriginal brief. Therefore, an effective bank of cross-referenced musicalelements that are contextually related to each other in the sense of“form” would beneficially facilitate effective generative compositionfor alignment with, for example, a visual sequence or the building of amusical program (such as occurs within film score development, TV orstreamed advertising and “spin” classes that choreograph cyclingexercise to music to promote work rates).

Interestingly, there is rarely a record of the crafting that went intoany compositional decisions, although some do exist and provide greatinsight into the compositional process (Ledbetter, 2002) (Norris, 2001)(Cooper, 1992). Mostly, we are just left with a single score orperformance, leading to an attitude of idolisation for the chosen notes;that is, notes that made it into the final manuscript that appearselected from a perfectionist standpoint. Evidence of the alternatives acomposer may have taken paint a picture of compositional craft andchoice that inevitably led to certain decisions of an arbitrary nature.In (Meeker, 1978), John Williams states that he had 97 differentversions of what became the five-note theme to Close Encounters(Phillips & Spielberg, 1977). These were grouped into four groups ofvariations initially, which were reduced and further refined from therethrough discussions with the director Steven Spielberg until he arrivedat the famous five note melody that is known. However, William's ownremarks nevertheless did not stop individuals writing about the apparentmathematics and physics-related perfection of his, and the director's,final choice for those five pitches in a particular chord, withparticular timing and note duration. To Williams, it was clear that thiswas a set of notes no better than many others; however, they were thechosen ones that others have come to believe were in some sensepreordained and, arguably, those with best “good form”.

As another example, an interactive game provides no tailoreduser-experience with respect to the accompanying musical score.Presently, “it is what it is” for the particular aspect of the game orscene in a game and just reflects base programming. Should there be aneffective generative process, then the sound experienced in terms ofmusical textures can provide an enhanced indication for the user asviewed from the emotional perspective of the on-screen avatar. Forexample, it would be an immersive experience for a player to be exposedto a user-dedicated specific musical segment that reflected growingemotional or physical conditions of the player's in-game avatar.Currently, gaming systems provide no audible suggestion of in-gameissues that the avatar is facing/experiencing and this is to thedetriment of the physical player experience. The problem, however, isthat each player journey is unique so how does a relevant tailored andmeaningful sound experience get generated on-the-fly? And, in fact, cansuch a sound experience be tailored to music that has particularconnotation and relevance to a specific user? At the moment, anyaccompanying game-related score is simply a generic path that may haveno emotional connection to the player and, indeed, the score mayactually not emotionally resonate with the player or actually may bedisliked by the player.

Generative music compilers do exist. These existing systems typicallyuse some form of Markov process to generate chords, but all have aseries of algorithms that produce different notes across differentinstruments. The problem with the prior art approaches is that theysupport little if any creativity and little if any ability to manipulatecompositional content. In fact, the prior art approaches all generallyproduce compositions that sound the same because all generatedcomposition is based on a fixed number of predefined instrumentaltemplates. The consequence of this straight-jacketing approach is a lossof musical texture. This is a significant problem which diminishesusability because of the resultant sameness.

There are various methods for writing chord schemes that have beenimplemented over the years (C. Johnson, Carballal, & Correia, 2015;Lerdahl & Jackendoff, 1996; Nierhaus, 2009). The aesthetic valuation forany given method is based on the developer's artistic requirements,justifications, post-rationalisations, or simple tolerances. Experiencein fact shows that it can be considered acceptable for any chord tofollow any other chord given enough context in the surrounding harmonicprogression. When choosing a chord to follow another one, if thiscontext is ignored and we only look for evidence of the sequence in anexample, we find ourselves in the position whereby chord schemes simplybecome a randomised sequence.

Whilst the present invention relates to a signal processing of a soundsignal especially for use in a generative sense, in order to providefurther context it is appropriate to provide a working basis for theterminology that is used by musicians and which is relevant to specificembodiments and implementations of the invention. In this respect:

-   -   In Western musical theory, a cadence is a melodic or harmonic        configuration that creates a sense of resolution (finality or        pause), especially since any cadence has decreasing emphasis. A        harmonic cadence is a progression of (at least) two chords that        concludes a phrase, section or piece of music. And a rhythmic        cadence is a characteristic rhythmic pattern that indicates the        end of a phrase. A cadence can be weak or strong depending on        its sense of finality. While cadences are usually classified by        specific chord or melodic progressions, the use of such        progressions does not necessarily constitute a cadence; there        must be a sense of closure as at the end of a musical phrase.        Generally, harmonic rhythm plays an important part in        determining where a cadence occurs. Cadences are also strong        indicators of the tonic or central pitch of a passage or piece        of music.    -   In music, the tonic is the first scale degree of the diatonic        scale (the first note of a scale) and the tonal centre or final        resolution tone that is commonly used in the final cadence in        tonal (musical key-based) classical music, popular music, and        traditional music. In the do solfège system, the tonic note is        sung as do. More generally, the tonic is the note upon which all        other notes of a piece are hierarchically referenced. Scales are        named after their tonics: for instance, the tonic of the C major        scale is the note C. The term tonic can also be referred to as a        the keycentre. The local tonic, e.g., Cm or Bb, provides both        the first and last notes of the scale.    -   A triad formed on the tonic note, the tonic chord, is thus the        most significant chord.    -   A chord is a series of pitches played in parallel with each        other and which are tied to a keycentre. In terms of function,        the mind makes use of a chord to predict where it is in the        composition. A chord does not in its own right have any        lexicological meaning because musical meaning is derived from        the syntax, i.e., the sequence of chords.    -   A chord scheme is a chain of chords.    -   A metachord scheme are the principals of how a chord scheme is        written.    -   Major and minor scales are two of the most popular and commonly        used scales in western music, with a set of notes each with a        distinct pitch forming the scale. Major and minor scales are        variations of the diatonic scale in which there are pitch        intervals a five full steps and two half steps, with the        relative pitch/physical displacement of the third note        determining whether the scale is major or minor. This third note        makes the major scale brighter and more cheerful sounding while        giving the minor scale its characteristic sadness, melancholy        and darkness. In a major scale, the third note is one note        higher than the minor 3rd note. The pattern of steps in a major        scale has note spacing WWHWWWH (where W representing transition        of a whole note and H representing transition of a half note),        whereas the pattern in a minor diatonic scale has note spacing        WHWWHWW. In convention Western music, any major or minor key        will have seven degrees/notes in its scale, i.e., notes A to G.

Whilst the inventive concepts—of which there are many—will now bedescribed in considerable detail, the following description ofadditional musical terminology may further assist.

Particularly in Western music, the relationship between chords isdefined by the degree of scale. The degree of scale refers to theposition of a particular note (having a particular pitch) on a scalerelative to the tonic, i.e., the first and main note of the scale fromwhich each octave is assumed to begin. In music theory, a diatonic scaleis any heptatonic scale that includes five whole steps (whole tones) andtwo half steps (semitones) in each octave, in which the two half stepsare separated from each other by either two or three whole steps,depending on their position in the scale. This pattern ensures that, ina diatonic scale spanning more than one octave, all the half steps aremaximally separated from each other (i.e. separated by at least twowhole steps).

An octave is the difference in pitch between two notes where one hastwice the frequency of the other. Two notes which are an octave apartalways sound similar and have the same note name, e.g., C, while all ofthe notes in between sound distinctly different, and have other notenames e.g., D, E, F, etc. Notes naturally fall into groups of twelve,which are all one octave apart from each other. An octave thus comprises12 equal semitones, with each semitone therefore having a frequency stepin a ratio of 2^(1/12) to the earlier frequency.

Further, it will also be appreciated that the choice of the note withina chord leads to its classification. For example, a three-note chord(which incidentally is a “triad”) can have varying note spacing betweenthe three notes of:

for a minor triad, 3 semitones followed by 4 semitones;for major triad, 4 semitones, followed by 3 semitones;for an augmented triad, 4 semitones, followed by 4 semitones; andfor a diminished triad, 3 semitones, followed by 3 semitones.

Whilst not wishing to teach your grandmother to suck eggs, a dominant7th is where the (piano) chord includes a fourth note that is adegree/scale note down from the 8th (i.e. the repeating note in the nextoctave), whereas a major 7th is where the chord includes a fourth notethat is a semitone down from the 8th.

Clearly, as will be understood, a full orchestration for multipleinstruments will have different scores for each instrument, withdifferent instruments having different numeric representations on theMusical Instrument Digital Interface protocol (MIDI) scale. For example,middle C has a value of 60 (representing a real-world frequency of261.63 Hz using contemporary tuning of A=440 Hz).

Instruments have idiomatic restrictions. For example, a conventionallytuned 4-string bass guitar, the lowest MIDI value is position 28.Conversely, a violin will only generally be able to play two notessimultaneously with these having a lowest note having a MIDI value 55.

Returning to the underlying technical problems associated with effectiveautomated generative composition, another issue faced by the musicindustry is how best to augment the listener/user experience, especiallyon a personal/individual level. Indeed, it has long been recognized thatthe contextual relevance of or relationship between a piece of music andan event brings about recognition or induces a complementary emotionalresponse, e.g., a feeling of dread or suspense during a film or aproduct association arising in TV advertising.

Tailoring a generative sound experience to a narrative articulated by anend user having no credentials in composition would be advantageousprovided that the composition was quickly generated and of a discerniblestandard. However, in short, for automated generative composition, thereis presently no effective way to assess “form” in a sound signalcomprised from selectively linked musical phrases typically expressed interms of bars, or indeed how a procedure for generative composition canbe automated to avoid “bad form” and thus to impose the relatedconsequences on human physiology and state of mind.

SUMMARY OF THE INVENTION

In overview, a generative composition system reduces existing musicalartefacts to constituent elements termed “Form Atoms”. These Form Atomsmay each be of varying length and have musical properties andassociations that link together through Markov chains. To provide myriadnew composition, a set of heuristics ensures that musical texturesbetween concatenated musical sections follow a supplied and definedbriefing narrative for the new composition whilst contiguousconcatenated sections, such as Form Atoms, are also automaticallyselected to see that similarities in respective and identifiedattributes of musical textures for those musical sections are maintainedto support maintenance of musical form. Independent aspects of thedisclosure further ensure that, within the composition work, such as amedia product or a real-time audio stream, chord spacing determinationand control is practiced to maintain musical sense in the newcomposition. Further and additionally, a new and complementary butindependent technical approach structures primitive heuristics tomaintain pitch and permit key transformation.

According to a first aspect of the invention there is provided agenerative composition system, comprising: an input coupled to receive abriefing narrative describing a musical journey with reference to aplurality of emotional descriptions for a plurality of musical sectionsalong the musical journey; a database comprising a multiplicity of musicdata files each generating, when instantiated, an original musical scoreand wherein each original score is partitioned into a multiplicity ofidentifiable concatenated Form Atoms having self-containedconstructional properties and where each has: a tag that describes acompositional nature of its respective Form Atom; a set of chords in alocal tonic, and a progression descriptor in combination with a formfunction that expresses musically one of a question, an answer and astatement, and wherein musical transitions between Form Atoms are mappedto identify and then record established transitions between Form Atomsin multiple original scores and such that, within the system, groupsexist in which Form Atoms are identified as having similar tags butdifferent constructional properties; and processing intelligenceresponsive to the briefing narrative and coupled to the database,wherein the processing intelligence is arranged to: assemble agenerative composition having regard to the briefing narrative throughselection and concatenation of Form Atoms having tags that align withemotional descriptions timely required by respective ones of theplurality of musical sections; and select and substitute Form Atoms fromdifferent original scores into the generative composition, thesubstitute Form Atom: derived from any original score; and having itscompositional nature aligned with the emotional descriptions.

The database may include heuristics in the form of meta-data containinginformation explaining how to reconstruct original musical artefacts aswell as alternatives thereto.

The Form Atom may be assembled into a string of form atoms that generatea string of chord schemes with associated timing.

The system can include chord spacer heuristics arranged to distributechords across a stipulated time window.

The system intelligence may be arranged to process chord schemes toinstantiate textures where texture notes are derived from chords andtheir associated timings.

Each Form Atom has minimal length and different Form Atoms may embodydifferent musical durations.

In one embodiment, a subset of the tags may be semantically identical.

In another embodiment, each Form Atom never includes a tonic in a middlesection of the Form Atom.

Each Form Atom will have a specific set of chords in a local tonicexpressed as interval distance relative to the local tonic having bothpitch and tonality.

In an embodiment, the Form Atom stores a chord type and a chord's bass.

In an embodiment, the database store lists of Form Atoms that are linkedto lists of preceding or following Form Atoms through Markov-chainassociations that identify, from a corpus of artefacts, priortransitions that have worked musically with good form.

Form Atoms provide harmonic structure and an ability to generateharmonic structures that obey compositionally good musical form.

Form Atoms may have associations to a list of mapped textural componentswhich define texture for the composition and which permit, whenselectively chosen and written with chord scheme chains, maintenance oftextural continuity in the generative composition.

In another aspect of the invention there is provided a method ofgenerative composition, the method comprising: receiving a briefingnarrative describing a musical journey with reference to a plurality ofemotional descriptions for a plurality of musical sections along themusical journey; assembling a generative composition having regard tothe briefing narrative through selection and concatenation of Form Atomshaving tags that align with emotional descriptions timely required byrespective ones of the plurality of musical sections; and selecting andsubstituting Form Atoms from different original scores into thegenerative composition, the substitute Form Atom: derived from anyoriginal score; and having its compositional nature aligned with theemotional descriptions; and wherein each original musical score ispartitioned into a multiplicity of identifiable concatenated Form Atomshaving self-contained constructional properties and where each has: atag that describes a compositional nature of its respective Form Atom; aset of chords in a local tonic, and a progression descriptor incombination with a form function that expresses musically one of aquestion, an answer and a statement; and mapping musical transitionsbetween Form Atoms to identify and then record established transitionsbetween Form Atoms in multiple original scores and such that groups ofForm Atoms exist in which Form Atoms are identified as having similartags but different constructional properties.

In a further aspect of the invention there is provided a method ofanalysing a musical score containing a plurality of musical sections,the method comprising: identifying the presence of an emotionalconnotation associated with a musical texture in the plurality ofsections and wherein the musical texture is represented by a pluralityof identifiably different compositional properties, and wherein: i) themusical texture has an emotional connotation; and ii) each musicaltexture of any musical section is expressed musically in terms of thepresence of musical textural classifiers selected from a set containingmultiple pre-defined musical textural classifiers and such that: a)different musical sections may include a differing subset of pre-definedmusical textural classifiers; b) for a given musical section, eachpre-defined musical textural classifier has either zero or at least onecomponent to that textural classifier and wherein each component that ispresent is further tagged as either a musical accompaniment or a musicalfeature and where each musical textural classifier that has a componentpresent possesses: i) either no musical feature or a single musicalfeature, and ii) one or more musical accompaniments; and c) differentmusical sections can have a common descriptor or a similar descriptorhaving an association with the common descriptor, but at the same timedifferent musical sections possess differing subsets of musical textualclassifiers or differing subsets of components in the musical texturalclassifier.

The textural classifier may be selected from a group comprising at leastsome of melody, counter-melody, harmony, bass, pitched rhythm,non-pitched rhythm and drums.

A musical feature is a salient musical component in musical texture; andcontains information about musical tension and release within themusical section and which tension and release would be musicallycontextually destroyed if the musical feature were to be combined withanother musical feature in the musical section and in the samepre-defined musical textual classifier. An accompaniment does notinterfere with another accompaniment or a feature in any specifictextual classifier of a musical section and can be added or removedselectively to thicken or thin the texture of the musical section.

In yet another aspect of the invention there is provided a method ofproviding texture in an automated generative composition process, themethod comprising: generating at least one chord scheme to a narrativebrief, wherein the chord scheme is based on Form Atoms and the narrativebrief provides an emotional connotation to a series of events; and applya derived texture to the at least one chord scheme to generate acomposition reflecting the narrative brief.

The method may further comprise identifying absence of a texturalnarrative in a first musical section concatenated with a second musicsection having a texture profile; and filling the first musical sectionwith at least one component that is a musical accompaniment or a musicalfeature selection wherein the at least one component is based on one of:history of preceding textural classifiers and a continuation of adominant one of the textural classifiers, else a logical bridge betweena destination subset of pre-defined musical textural classifiers basedon intensity of respective subsets.

Effective generative composition, according to the various componentaspects of this disclosure, thus leads to a tangible technical effect,particularly through the production of a generative work that has “goodform”. The embodiments achieve this through a categorization process inwhich technical properties linked to Form Atoms, of non-standard varyingduration, are extracted and stored relative to a descriptor ofexpressive qualities of each Form Atom. A relationship map isestablished between different Form Atoms such that the technicalproperties exhibited by one Form Atom can be concatenated with thoseproperties of an adjacent Form Atom in a fashion where the transition inmusical terms between adjacent Form Atoms has perceptibly good form.This approach underpins the ability to produce automated generativecomposition.

The present invention, amongst other things, functions to reduce chordsto their relational position to the base tonic, while maintaining pitchrelationships arising in any transposition between differentkeys/tonics. The chain of transitions is then maintained. Putting thisdifferently, in any musical key in the preferred implementation, therelationship between chords is expressed by the degree of the scale.Thus, regardless of the octave, in the key centre of F, an F note in thescale would be expressed as a value I, a Bb as a IV and a C as a V. Thisapproach therefore leads to an equivalency between chord schemesirrespective of the chosen tonic and is maintainable across both majorand minor scales (or any chosen degree of scale that departs from theexemplary context of a 7-note Western scale as used herein).Consequently, by reducing notes within chords to their relationalposition relative to the base tonic means that relative constructionalcontext of any chord is maintained irrespective of transposition to adifferent tonic, i.e., the chain of transitions is then maintained. Thusin the exemplary key of C major on a piano:

Middle C on the piano would have a MIDI value 60 and position I,db on the piano would have a MIDI value 61 and position IIb,D on the piano would have a MIDI value 62 and position II,Eb on the piano would have a MIDI value 63 and position IIIb,E on the piano would have a MIDI value 64 and position III,F on the piano would have a MIDI value 65 and position IV,Gb on the piano would have a MIDI value 66 and position Vb,G on the piano would have a MIDI value 67 and position V,Ab on the piano would have a MIDI value 68 and position VIb,A on the piano would have a MIDI value 69 and position VI,Bb on the piano would have a MIDI value 70 and position VIIb,B on the piano would have a MIDI value 71 and position VII, andC (in the next octave and with a return to the tonic) on the piano wouldhave a MIDI value 72 and position I (again).

The preferred embodiments therefore work on the premise that every chordcan be measured in the context of its local tonic/key centre by aninteger, and that relationships can be established between chords ratherthan just sequencing of specific chords.

Advantageously, aspects of the present invention therefore analyse andthen parse music to deduce various heuristics permitting generation ofmusical textures as well as performance parameters and the buildingblocks required for assuring quality of final assembly/performance ofprocessor-originating generative work. A classification mechanism allowsfor different instrumental components to be used in differentcompositional contexts, thereby allowing brand new textures to becreated through combining principals of different compositions. Thebeneficial result is a generative composition that follows a brief,i.e., a narrative provided by a client, and which consequently ismusically relevant, formalistically variable (since, unlike the priorart approaches, it is not formalistically tied to a template) and whichhas audibly—and thus reward centre rewarding—good musical form.

Beneficially, based on processing music information retrieval techniquesand analysis supported by a processor-based system intelligence, such asa bespoke expert system, the present disclosure provides a multiplicityof complementary yet inventively different technical solutions. Theprocessing mechanisms function to compress an original musicalcomposition through a series of mathematical functions (having correctlyapplied parameters) that support both the reproduction of the originalcomposition/score as well as myriad other alternative generativecomposition that satisfy human requirements of predictive tension andrelease that stimulate the reward centre of the brain to promotedopamine release. In this respect, correct parameters amount to theapplication of mathematical choices based on developed core heuristics,i.e., rules, together with a sequential ordering of execution of thesecore heuristics. The invention applies an Occam's Razor approach, i.e.,generative mathematical functions should be the simplest to support theobjective reproduction of the original musical intent, to selection ofheuristics in the various generative aspects of the approach, such as in(a) pitch generation, (b) pitch transformation into a new tonic, (c)chord spacing that maintains the rate of play of generative chords inthe generative composition and (d) texture maintenance in the generativecomposition. Examples of such mathematical functions, of which there aremany disclosed in detail herein, can include the axioms that a bass notein transposition cannot be below the lowest note on a bass guitar or ascore for a transposed violin component can maximally only relate toplay two notes simultaneously.

Applications of the techniques of the embodiments and aspects of thisdisclosure can be employed in any music to video application, includingfilm score, advert production and gaming (especially in the context ofproducing a user-specific musical accompaniment that is generated toreflect player-selected music having direct player connotation to playeremotion(s)). Also, since the generative piece embodies “good form” andoriginality, the application of the technology can be applied to producea new composition for which lyrics can be written.

The present invention produces alternative generative musical works thatare equally satisfiable to the mind from a process that identifiescompatible musical elements from different musical sources/scores andconcatenates complementary generative heuristics/mathematical functions.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolour. Copies of this patent or patent application publication withcolour drawing(s) will be provided by the Office upon request andpayment of the necessary fee.

Exemplary embodiments of the present invention will now be describedwith reference to the accompanying drawings in which:

FIG. 1A is a diagram illustrating composition approach in the prior art.

FIG. 1B is a diagram illustrating compositional approach of the presentinvention.

FIG. 2A shows a prior art sketch of the final score to The High and theMighty.

FIG. 2B shows a prior art formal final score to The High and the Mighty.

FIG. 3 is a representation of texture classification and generativeassembly according to an embodiment of an aspect of the presentinvention.

FIG. 4 is a representation of texture classification and generativeassembly and in which an intermediate musical section has beenunspecified and “filled” to provide texture continuity according to anembodiment of an aspect of the present invention.

FIG. 5 is a hierarchical task flow for the generative compositionalsystem of a preferred embodiment.

FIG. 6 represents, according to an embodiment, assemblage of permissibleinter-Form Atom mapping relationships.

FIG. 7 shows the Affordances of a heuristic mechanism with hierarchicaland logical flow as practiced by the approach of embodiments of thepresent invention.

FIG. 8 is a schematic view of a preferred composition architecture andmethodology for generative composition.

FIG. 9 shows, according to a preferred embodiment, how a singlecomposition is parsed into a set of trees with viable Form Atombranches.

FIG. 10 is a schematic representation of texture generation according toa preferred embodiment of the present invention.

FIG. 11 is a screen shot of a graphical user interface for a pieceannotation system according to one embodiment of the present invention.

FIG. 12 is a chord placement chart representing a spacing heuristic foruse in one embodiment of the present invention.

FIG. 13 is a sequential Form Atom template for use in one embodiment ofthe present invention.

FIG. 14 is a portion of The Quidditch Match musical score by JohnWilliams annotated for reduction and analysis according to animplementation of the present invention.

FIG. 15 is an intervallic template representing a loop of sequence FormAtom 3, with escape Form Atom 4, derived from The Quidditch Matchcomposition according to an implementation of the invention.

FIG. 16 is a template representing a Form Atom 6 sequential cadencederived from The Quidditch Match composition according to animplementation of the invention.

FIG. 17 is a template representing sequence and escape phrases 7 and 8derived from The Quidditch Match composition according to animplementation of the invention.

FIG. 18 is a musical score of a four-bar section of detache stringwriting enhanced according to one implementation of the invention withassociated colour labels that indicate note pitch.

FIG. 19 is a musical score of the first two bars of the Prelude in CMinor by Johann Sebastian Bach modified according to one implementationof the invention by highlighting syntactic structures and note pitchesaccording to a predefined colour scheme.

FIG. 20 is a table showing degrees of the scale of semiquaver 3 withrelation to the local dominant of the corresponding bar, in an analysisof texture according to the invention.

FIG. 21 is an exemplary diagram according to an implementation of theinvention that expresses musical notes within Bars 1 to 3 of the Bachprelude as a numerical array.

FIG. 22 is an alternative exemplary diagram according to animplementation of the invention that expresses musical notes within Bars1 to 3 of the Bach prelude as a numerical array.

FIG. 23 is another exemplary diagram according to an implementation ofthe invention that expresses musical notes within Bars 4 to 6 of theBach prelude as a numerical array.

FIG. 24 is a table illustrating changes in the pattern in the bass atsemiquaver 5, including direction of the pattern, the chord component onwhich the 5th semiquaver in the bass lands, and the 5th's position ineither the Treble T or bass B.

FIG. 25 is another exemplary diagram according to an implementation ofthe invention that expresses musical notes within Bars 7 to 9 of theBach prelude as a numerical array.

FIG. 26 is another exemplary diagram according to an implementation ofthe invention that expresses musical notes within Bars 10 to 11 of theBach prelude as a numerical array.

FIG. 27 is another exemplary diagram according to an implementation ofthe invention that expresses musical notes within Bars 12 to 14 of theBach prelude as a numerical array.

FIG. 28 is an image of a Wilhelm Friedemann Bach manuscript copy ofJohann Sebastian Bach's Bar 14, C minor prelude 1, from the“Clavier-Buchlein version”.

FIG. 29 is an exemplary diagram according to an implementation of theinvention that expresses musical notes within Bars 15 to 17 of the Bachprelude as a numerical array.

FIG. 30 is an exemplary diagram according to an implementation of theinvention that expresses musical notes within Bar 18 of the Bach preludeas a numerical array.

FIG. 31 is a musical score representation of the Bach prelude accordingto an implementation of the invention that uses color-coded heuristicsshowing hierarchical flow and highlighted points of entropy.

FIG. 32 is a musical score representation according to an implementationof the invention of all possible combinations (spanning an octave) ofmajor and minor triads with C and Eb as the top extensions.

FIG. 33 is an image of a keyboard representation showing possible noteswithin textures of Bars 19 and 20 of the Bach prelude according to animplementation of the invention.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

The extensive nature of this application and the invention lends itselfto being broken down into an overview, followed by explanatory sectionsand then followed by a worked example of the application of the signalprocessing approach and the application of the functions to a specificexample. Within this application, the system may be referred to as the“Heresy generative system”, “generative composition system”, or otherappropriate descriptive tag for a computer-implemented system thatoversees a real-world application of a new mathematical analysis andre-assembly approach within an applied technical process applying aTuring equivalency that results to an improved technical output.

The principles behind the “Heresy generative system” revolve around ashift from how we traditionally view compositions and the compositionprocess, and treats music (and the related signal processing of audiosignals) as a fluid non-static entity that never has a final fixed statethat cannot be changed.

It is important to understand the requirements involved in creating a“brief” before considering how each aspect of the generative system ofthe preferred embodiments interact to create a new score from existing(analysed) artefacts. The brief itself is a set of compositionalrequirements that are the backbone of the generative system. Thedescription will then consider the generative approach of the variousembodiments and aspects.

The invention considers, as a corpus, potentially all compositions as asource for analysis, reference and input into the generative system.Through this process, the invention functions to extract (either throughdigital analysis through signal processing by AI or processor-basedintelligence or otherwise by a musicologist) certain specificcompositional principles from a given composition or multiplecompositions, thus allowing the invention to blend principles fromdifferent works into one distinctive/discrete meta-composition. Applyingan Occam's Razor based approach, these compositional principles areexpressed as a set of heuristics/rules that can subsequently create newgenerative works.

With regards to the Heresy generative system, it is understood thatdifferent keywords in a brief potentially have different meanings todifferent users. Therefore, it is preferable that generic terms thathave little semantic meaning to the concept they are tagging are used,in order to give a noun to a category, whilst still allowing attachmentof one or more keyword to a personal set of meta-tags that meansomething to a user alone. Natural Language Processing “NLP” can beemployed to derive a processible data for a usable descriptor of amusical section.

An effective categorisation strategy may be the Estil method of vocaltraining (Klimek, 2005). This abstract connotation-labelling methodoffers a viable alternative to trying to attach words with semanticmeaning to music, the pitfalls of which are highlighted in (G. A.Wiggins, 1998).

The system of the invention and preferred embodiments provide aframework for crafting iterations in composition. It offers a way forusers to state an intent (in the form of an inputted narrative or briefthat is interpreted and correlated to heuristics and thus salientmusical sections that can be concatenated together in an auditoryseamless fashion), and then, indeed, to adjust quickly the output fromthis briefing specification. In other words, the system of the presentinvention offers the ability to define a set of compositional ideas,before auditioning them and listening to how effectively theycommunicate the original intention. Nevertheless, the chosen ones willchange every time the system is asked to generate a new composition,whilst form is protected. The inventive approach takes this principleone step further in that it offers the ability to see which generativeexpression is potentially “wrong”. More particularly, through criticalanalysis and commentary of the system's output, it is possible toidentify (considering the original intention/instruction/brief) exactlywhich heuristic produced a wrong chord, note pitch, length, position,voicing, voice leading, textural clash or emotional connotation. It isthen possible to reflect this criticism in the heuristics themselves,altering how they make their decisions to fit better the compositionalintention, iteratively refining the heuristic expression of the originalconcept. Alternatively, whilst the system can generate perfectlyreasonable material, there are instances where this result could bebetter aligned with the original intent. This gives two things: firstly,a new compositional idea that can be post-rationally meta-tagged as adifferent concept; and secondly, an insight into how close one'soriginal intention may be to other compositional ideas and indeed thegenerative work.

The system of the present invention makes a shift of roles fromtraditional film-scoring methods. Where composers have traditionallyrelied on technological tools by programmers and engineers (such asstreamers and click-tracks), and sequencing software for demoing theirmaterial; and whilst commissioners have taken a selective role inchoosing material presented to them, such as Steven Spielberg did withthe themes for both Indiana Jones (Laurent, 2003) and the CloseEncounters five-note motif (Meeker, 1978), the system of the presentinvention shifts these roles; this is reflected in the comparison ofapproaches shown in the commissioner/user/composer/programmerdelineations of FIGS. 1A and 1B.

With the present invention, the composers themselves become both theprogrammers and the users. Composers now use the tool to create theheuristic processes that can be used by other users, thus taking on thetechnical role of programmers, whereas the commissioners themselves canbecome composers, as users of the generative tool.

The approach underlying the present invention is based on anunderstanding of composition, and particularly the act of composition,in a conceptually different way, namely: showing how the next note inthe audio signals follows an earlier note (as expressed in rulesassociated with the generation thereof and the length of a fundamentalmusical component that expresses fundamental audio signal components ofa musical section) a rather than what the note actually is. In thisparadigm, the principle of composition requires a method of analysis,with iterations of generated heuristics applied to refine the conceptfor composition.

According to the present invention, a processor-based system and relatedmethodology differs from systems of earlier approaches in that thepresent invention makes each of the processes, decisions and weightingfactors (that go into composition) the core on which the system canabstract the principles for how to generate these new compositionalworks. Particularly, rather than using a suite of parameterisedgenerative systems that present components whose compositional input isall but complete, the system of the present invention break downscomposition from scratch and creates generative mechanisms for thespecific piece.

Axiomatically, the present invention asserts that:

1. Fewer heuristics that can achieve the same result are more desirable.This is Occam's Razor and by making heuristics easier to understand thisapproach makes them easier to adapt and easier to build on with futurerules applied by the processors and functionality of the presentinvention.

2. A linear increase in heuristics encompasses an exponentiallyincreasing number of works. In short, new compositions preferably shouldincreasingly incorporate past analytical components, and therefore giveincreasing compression progress to a universal set of heuristics thatexplain previous and future compositions.

3. New heuristics must explain more than one phenomenon. If a set of newrules only explains one core compositional component from a specificpiece, then this is a bespoke ruleset and should be omitted untilevidence from the corpus can provide further examples of where theheuristics are appropriate. This avoids over fitting rules to analysisof composition, and causing bloat and noise in the pursuit of seeking amore unified understanding of composition. In practical terms, fewerrules will be required to explain new compositions by (at least) thesame composer, or for those compositions that are connected throughsimilarity in genre or time.

When a piece is analysed and generative heuristics are created from it,these will have a specific flavour, and can be considered a “pack”. Aheuristic pack may produce piano preludes in the style of Bach, oraction movie music in the style of John Powell. These packs can then bemeta-tagged with information about the intention of the content and itsemotional connotation(s).

In this way, music composed by the generative framework of the presentinvention never has a generic and identifiable sound in itself, but itsheuristic packs most definitely will. The functional tool thus reflectsa generic expression of composition with a measurable output that allowsfor refinement towards greater simplicity and higher diversity ofoutput. This in itself is significant to the compositional processespecially in the context of automated generative composition havinggood form.

The present invention, as will become apparent from the more detailedexplanation below and herein of the various interactive components thatsupport automated generative composition, is capable of predicting theimmediate path for a new composition at a specific point, therebyoffering a new mechanism in the field of composition for reflection onpractice, and refinement of the categorisation of emotionalconnotations.

Section A I. Meta-Composition: The Briefing Mechanism

Music is synced to film for a variety of reasons. Whilst “synced” music,i.e., music which sits within the diegesis, is typically heard by thecharacters as part of the story, non-diegetic music, i.e., music thatsits outside the story and comments on it, acts in a variety of ways tobring out certain properties of the film.

In the case of synced tracks, that is tracks that have been pre-recordedby an artist and then superimposed to accompany the action (pop, rap,and such the like), these tracks are often the starting point in theediting room and form the basis of the pace and style of the cut. Thesebring sub-cultural identities to the film, grounding it in genre, orlending the connotations of a certain culture to the film. Aquintessential example of this is the use of “Hotel California” by theGipsy Kings in The Big Lebowski. In the scene that introduces thecharacter of Jesus Quintana (played by John Turturro), the viewer isgiven a reinterpretation of the original song, which itself has alaid-back, and somewhat melancholy treatment in both lyrics and musicalfeel. This new interpretation has an energetic and spirited quality,giving connotations that the character Jesus views the environmententirely differently to the narrative's discourse so far: this is ajuxtaposition that is highlighted further by a montage of slow-motionshots that accompany the fast-paced music.

In the case of the non-diegetic music being custom written by a scoringcomposer, s/he may choose a discourse via a textural palette to achievea specific effect such as this juxtaposition in the Jesus Quintanaexample, but will also be looking to help the pace and flow of the filmthrough appropriate tempo and time signature mapping, as well as tofollow the story on screen until preceding narrative peaks to createtension.

Embodiments of the present invention therefore provide an interface andfunctionality to a user that allows for the briefing of the aboveelements. There are several methods that can be considered asappropriate, including but not limited to:

1. A written brief from a spotting session with time-codes for wherecues will start and stop, as well as the connotations that each cue willhave, complete with any hit points that the director/composer haveagreed on.2. A full score for the film.3. A short score, or “sketch”, on a limited number of staffs, thatcontains the basic compositional material for orchestrators to use.4. A partially graphical score used to make notes across a mapped-outtimeline that gives the composer, or orchestrators s/he trusts, notes onthe desired sound, texture, and harmony. In this situation, thecomposer's or orchestrator's ability to interpret and understand thedirections is an intelligent parsing mechanism that the brief relies onto obtain a result. This discrepancy between sketch and final score ishighlighted by the reconstruction of the score to The High and theMighty as seen in FIGS. 2A and 2B.

Whilst the above list is not comprehensive, it provides an indication ofthe requirements for a tool that allows briefing. There are, however,components in the briefing that are significant and include some or allof:

1. The ability to map pace across time. This clearly points to the useof a musical time ruler rather than a standard minutes, seconds, andframes ruler. This ruler should be adaptable through tempo and timesignature changes to map out the pace of, for example, a film or aspectof an adventure/quest game whether multi-player interactive andirrespective of the game being streamed or remotely accessed.2. A system to specify hit points, and the associated connotation thatthe hit point should have.3. A method for specifying textural elements and their connotations atdifferent points in time.4. A list of discourses that can be chosen, which bring with themsub-cultural properties: “Cuban Montunos”, “LA Urban”, etc. This mayalso manifest itself as the distinctive sound of certain composers, suchas “John Barry”, or of films themselves such as “The Bourne Identity”movies.5. A method of setting the compositional pace, including one or more of:(a) The number of chords across time; (b) Modulations and shifts intonality; and (c) Emotional connotation keywords that can be associatedwith different chord scheme properties: (i) Use of pedal notes as chordschange; (ii) The use of a cycle of fifths to move through key centres;and (iii) Functional properties of a chord scheme, such as the beginningor end of a cue.

The last item in this list, namely the method of setting compositionalpace, gives a hint at the structural hierarchy that the system of theinvention uses to compose generatively, as explained in more detail inSection B below. It implicitly is stating that all pace andcompositional form comes from specifying a chord scheme and itsfunctionality across time. The chord scheme's requirements are thepillar on which we build the brief, and hence generate output.

II. Chord Scheme Requirements

The complete system of the present invention is based on aspects oftextural and melodic output as harmonic sequences of chords. Ittherefore uses such sequences to form sections of the piece and set itspace.

Chord schemes, in the case of the generative system of the variousembodiments and aspects, therefore have two distinctive properties: (i)their form function, and (ii) their emotional connotations.

From a form perspective, the system is arranged to permit annotation ofinformation/stored data for any given section to reflect that this data:

1. Is the current section starting, ending, or in the middle of the cue?2. Focuses on the piece's tonic, or whether there is a need to move to adifferent key centre by the end of a section?3. Represents a section that should be modulated, i.e., is there a needfor a local tonic in the next Form Atom (see below) to be different fromthe local tonic of the current Form Atom (i.e., musical building blockof potentially variable length determined by the surrounding context andmusical properties and transitional points of the Form Atom)?4. Stipulates the chord density (number of chords over musical duration)for a given section?

This briefing of desired form functionality of a specific section bringswith it information about how the chords should be written in relationto the piece's tonic, whether there should be a movement, via amodulation, at that point to arrive at a new key centre in order to movethe piece on into a different subsection of the composition/film.

Functionality in the system intelligence and its interpretationalcapabilities (see below), when combined with the above form function,provides the ability to set the number of chords within a given section,thereby allowing comprehensive shaping of the form and direction of thegenerative composition.

No matter what generative technique is used to create the form andchords of a new piece, there remains a need for the user to brief theemotional connotative elements that the programmer/composer wants thepiece to take. Providing context, when it comes to expressingconnotation within film composition, composers try to draw on theplethora of discourses and codes that are within our western culture.However, when dealing with the subject of lexical meaning and itsdescription of music, little consensus exists even from individualswithin the same sub-culture. This is because individuals each havedifferent interpretation of their cultural coding.

In terms of reference materials in the form of nuggets of usable musicalsections, the system is functionally arranged to reference differentcompositional components' connotations with meta-tags that make theirreproduction easy, but which leave their interpretation open to theuser's briefing/narrative. As indicated previously, the briefing may beprocessed using NLP techniques to cross-correlate coded musical sectionswith similar or identical language expressed in the narrative that isinput to the system. NLP techniques are well-known. In this way, a usercan bring their own interpretation to the system's ability to write agenerative composition independently based only on the brief as input,coded and correlated to sections of music having associated connotation,without being hindered by a programmer's perspective on what themeta-tags associated with or attached to the musical segments shouldalways apply. Clearly, emotional connotations take the form of genericvariable keywords (or short key phrases) which have user specificmeaning. These are initially named as Mode 1 . . . Mode n, but can bechanged depending on the user's preferred lexical meaning. Compositionalheuristics (such as methods for creating specific chord sequences,textures, melodic contours, chord-spacing heuristics, note generators,and rhythm generators) have these keywords attached to them. Thegenerative mechanism operates to select appropriate heuristics to createthese connotations at each instance in the timeline where they arerequested by the user.

III. Texture Requirements

Having established how to meta-tag connotations to specific musicalgenerative heuristics, the system of the various embodiments provides amechanism that maintains musical texture and particularly constrainsrequests for insertion of adjacent musical components (e.g., Form Atoms)that would clash, such as asking for seven melodies at the same time orthree bass lines.

It is, however, entirely possible to have three bass lines at the sametime. John Powell's cue “To The Roof” from The Bourne Supremacy hasexactly this: we hear a driving bass line in the synth bass, accompaniedby the double basses playing sustained long notes in the bottom of thestring texture, whilst there is a percussive effect every bar on thefinal three semiquavers of the bar and the first beat of a new barwhereby a bass player drags the fingers across muted strings. Inisolation alone, any single one of these bass lines would work as aviable bass part, but here the texture calls on all three to make afinal effect that neither contradicts the harmony nor clashes in sonicspace.

The system intelligence firstly generates a set of heuristics andapplies a technical approach to the identification and use of a set ofmusical components [for instruments], such as stings (e.g., a viola),offset horns, a harp arpeggio, pizzicato-bass. Identification can beachieved using Music Retrieval technologies to create a MIDIrepresentation of the original score, or simply the original scoreitself stored in MIDI format. There can be one or more musicalcomponents that then contribute to define a set of textural classifiers,such as [but not limited to] melody, counter-melody, harmony, bass,pitch rhythm, non-pitch rhythm and drum/beat and other musicalcharacteristics as will be appreciated by the skilled addressee. In thisrespect, reference is made to FIG. 3 .

Each of these musical instrument components is further classified,according to an aspect of the invention associated with final assemblyof a composition, to have one of two attributes, namely the componentmay either be a “feature” or an “accompaniment”. A (musical) feature canbe considered to give temporal sense, awareness and gravitas, i.e.,contributing significance, to a musical section. A musical feature isthus a salient sonic component in the texture space of the musicalsection, i.e., it itself contains information about tension and releaseand which information would be destroyed in the event that a secondfeature co-existed in a common textural classifier even if that secondfeature is played by an entirely different instrument. An accompanimentis complementary musical fluff that is inessential but provides richnessand tonality to a textural classifier.

There is also one or more semantic descriptors associated with eachmusical section, such as a Form Atom. The descriptors will generally bederived by a musicologist who has critiqued a musical section of anexisting piece of music and, indeed, within an overall corpus of musicalartefacts in a library.

Within each musical section, a musical component or collection ofmusical components (including multiple musical components in a singletextural classifier, such as harmony) can be grouped together andcorrelated/tagged with a semantic descriptor, such as “raunchy”, “warm”,“gritty/sleezy”, “floaty”, “pounding”, “victorious”, “reminiscent”,“calm”, “both smooth and reminiscent at the same time”, as well as withbroader semantic descriptors such as “loud”, “sexy”, “exciting” and moreother descriptive connotations, including “light Spring day” and“shimmery woodwind”. There are, of course, myriad semantic descriptions.Different musical sections may contain the same semantic descriptor or asimilar sematic descriptor that has some common descriptiveconnotations, but then again the same semantic descriptor in differentmusical section may have different instrumental components and/ordiffering numbers of instrumental components. The semantic descriptorsare therefore linked or associated, such as within metadata, to therespective musical section. Semantic descriptors can therefore beassociated with just a single instrument component, or otherwiseassembled from a subset of instrument components or groups of subsets(either mutually exclusive or overlapping) of instrument components orfrom groups of textural classifiers. The granularity is user-selectable.

Whilst it could be possible for the system to store the textureclassifiers for each section with each section or provide a directrecord, it is preferred that the system intelligence applies a set ofheuristics, e.g., computation parameters, to generate the respectiveattributes (having regard to historical records of what combination ofinstrument components are linked or closely associated with particulardescriptors).

With automated generative composition, the inventor has identified thatinstrument components within a particular textural classifier (e.g.,melody) cannot contain more than one instrument component that iscategorised as a feature. If this were the case, then features in thesame textural classifier would be mutually destructive. However, this isnot the case for musical components that are accompaniments.Consequently, a single textual classifier may contain zero or amultiplicity of instrument components acting as accompaniments but nomore than one (if any) instrument components fulfilling the role of afeature. Conversely, within a descriptor, multiple features may exist solong as the multiple features are distributed across the texturalclassifiers (and not within a single textural classifier.

In FIG. 3 , for example, the descriptor “pounding” in musical section 4of “Piece 1” is comprised from four (4) textural classifiers, namelybass, pitched rhythm, non-pitched rhythm and drums. It just so happensthat “pounding” is actually a subset of a more general descriptor“victorious” which further includes a melody as well as a harmony. Inthis example, the semantic descriptor “pounding” actually has eightindividual instrument components, with one being a feature component “F”in the bass textual classifier, two individual instrument componentsbeing accompaniments in the textural classifier pitched-rhythm, threeindividual instrument components being in the non-pitched rhythm ofwhich one is a feature and two are accompaniments, and two individualinstrument components being in the drums (textural classifier) on whichone is a feature (such as a floor Tom) and one is an accompaniment(e.g., a snare). For the sake of simplicity, the number of instrumentcomponents is represented in each textural classifier as either ablank/nothing (in absent), or the letter “F” for a feature or one ormore letter “As” to represent the number of instrument accompaniments.Looking now at “Piece 2”, one can see that there is no descriptor forits section 1, one descriptor in each of sections 2, 4, 5 and 6 wherethe counter melody in section 4 has no assigned descriptor and thus nocontribution of the connotation “warm”, and Piece 2 has two differentbut independent features for melody and harmony that both relate to thesemantic descriptor “calm”.

There is one further piece of information that can be derived, by theprocessing system of the invention, from the instruments components,namely musical intensity. Based on a comparison between sections, acount of the number of instances of feature and accompanimentsassociated with a descriptor and/or the entire musical section isinterpreted to provide an indication of intensity in that section. Inshort, the higher the count of components then the more intense and richthe section.

The system intelligence functions to look for commonality in descriptorsbetween musical sections and, importantly, the contributory nature ofthe components associated with each of those descriptors to identifyusable instrument components (or entire descriptors) that can complementone another across different musical sections in any future generativecomposition.

As intermediate summary, there may therefore be one or a multiplicity ofinstrument components and/or textural classifiers that can contribute toan overall texture for any musical section. Indeed, within a musicalsection, there may actually be zero, one or more sets of texturalclassifiers, with these having musical components that are treated bythe system intelligence to be mutually exclusive or complementary andwhich sets may be isolated, partially overlaid or layered so that onetextual classifier is actually a subset of another textural classifier.

Returning again to FIG. 3 , looking at musical section 3, the systemintelligence thus identifies the bass accompaniment to be usable forexpressing an emotional connotation of one or a combination of “gritty”,“sleezy” and/or “floaty”. The linkages (shown by dotted lines in FIG. 3) just show how, potentially, the system intelligence can insert musicaltexture derived from analysis of a musical corpus into a new compositionthat follows a briefing note pounding followed by warm and smoothfollowed by victorious and reminiscent, and with a time-varyingintensity that drops between the start of musical section 1 and the endof musical section 2, then levels off during musical section 3 beforesharply rising and then remaining constant in musical section 4 beforeagain sharply rising at the start of musical section 5 before tailingoff to zero intensity.

It should be noted that the musical sections are not representative ofdiscrete time scales and there may, in fact, be a multiplicity of FormAtoms present within each musical section.

Turning to FIG. 4 , there is shown a succession of musical sections40-48 for a first piece of music 49 and a succession of musical sections50-58 for a first piece of music 59, with the first and second pieces ofmusic forming a (limited) “corpus” of artefacts. For the sake ofexplanation only, the textural classifiers 60 have been restricted tofour, namely melody, harmony, bass and drums and are presented from theperspective of a simplified macro perspective (rather than with texturaldescriptors with sub-classifications and more complexinter-relationships). In FIG. 4 , contributory derivative musicalcomponents are drawn or assembled into the generative composition 70from similar descriptors analysed by the system and parsed fromindividual musical section in the corpus; the relationship is shown bythe lines with arrow heads.

A brief has been input into the processing system of preferredembodiments, such as through touchscreen or other computer interface.The brief stipulates an intensity pattern 62-66 for musical sections 1,3 and 4, but no narrative for musical section 2 that must thus be filledfrom all perspectives of the invention as described in totality herein,including texture continuity.

Dealing solely with the latter issue of texture continuity at thispoint, the system intelligence of the preferred embodiments firstlylooks to assemble a musical section that is both “rough and warm”. Thereis no corresponding overall texture having the descriptor, so theprocessing system assembles the components of “rough” from Piece 1 and“warm” from Piece 2. These are entirely complementary since they have nofeature in a common. The textual classifier and the overall intensity ishigh so there is no particular need for the system to reduce the numberof accompaniments. This therefore generates:

Rough and Warm Rough Warm Gen.Textr Mel. AAA FA AAAFA Harm. F A FA BassFA FA Drums FA FA

Ignoring the intermediate transition in the succeeding musical section,the third musical section is narrated as being “exciting”. There is, inthis respect, a directly corresponding texture that can be lifted frommusical section 3 of Piece 2. In musical section 4 of the generativework 70, there is also a corresponding pre-analysed “loud” texture atmusical section 3 of Piece 1. However, the system recognises thatadaption is required both to fill the unspecified space 80 betweenmusical sections 1 and 3 and to morph the texture in the generative workfrom reflecting “exciting” to reflecting “loud”.

Musical section 5 has no stipulated texture and so either represents atermination point for the generative composition 70 or a chance torepeat musical section 4 in totality or with a variation in, forexample, an accompaniment. These are design parameters executable by thesystem intelligence based on heuristical instruction.

Dealing with the fill, there are four alternative processes by whichfill can be accomplished by one or an appropriate and logicalcombination of:

1. Morphing from the components in a start texture to the requiredcomponents of the texture in the destination section. This can be asimple linear interpolation exercise;2. Fulfil a requested intensity brief stipulated by the user;3. Apply a Markov approach by analysing corpus of historically closestcompositions to identify the likely or permissible transitions betweentextural classifiers; and4. Work on the basis of selected intensity in terms of specific desiredtextural classifier, such as harmony.

In terms of user input of the preferences for unspecified musicalsections, a preferred embodiment includes a GUI that includes dial-downvalues for one or more user-selectable textural classifiers. Theuser/programmer is thus able to set relative intensity levels betweenthe multiplicity of textural classifiers, with the system intelligenceconfigured to apply comparative analysis to identify suitable candidatesfor direct in-fill or adaptation.

Looking again at the generative composition 70 and its texture needs,since the musical section 3 must include the prior analysed textualclassification for “exciting” in Piece 2, there is no choice other thanto maintain this exact textural structure because the texturalclassification fits. The first issue relates to the unspecifiedintermediate hope at musical section 2. It is generally desirable tomaintain features from a previous section, and it is also relevant toassess the level of intensity in the texture presented for “rough andwarm”;

this looks relatively high given the nature of the distribution of theinstrument components across all textural classification and alsobecause the resulting texture of rough and warm includes three features.Consequently, heuristics would generally dictate that a variation wouldbe required to begin the transformation towards the texture for“exciting” but it would be beneficial from a continuity perspective tomaintain a solidly associated texture from “warm” of Piece 2, but toreduce the accompaniment associated with purely the rough texture. It isnoticeable that significant musical components from the “rough”descriptor remain, although now diminished. To move in an alternativedirection, the system intelligence would—or at least could—considerretaining either contribution from bass and drums from the roughtexture, with this including continuation of either or both of theaccompaniment or feature components from the rough texture. However, inview of the brief drop in intensity, a fuller carry-over of theaccompaniments from musical section 1 is not preferable. However, thefeed-through of the feature from the drums through each of thesuccessive musical sections yields a degree of textural continuity. Inshort, the system intelligence looks to maintain as many contributinginstrumental components whilst having regard to the intensity changesand avoiding conflict between features that would class in the sametextural classification.

In summary, again, the processing system and logic treats featureswithin a musical section with a simple single rule. Any instrumentcomponent that realises a feature within a single textural classifierwill directly conflict with another feature in the same texturalclassifier and so that musical situation must be avoided to preserveoverall textural space. However, a textural classifier may have as manyaccompaniments as it wishes. This provides the ability to have multipletextural elements, whilst guaranteeing that any specific one thatprovides a salient feature to the texture will not be corrupted orinterfered with by others. In the aforementioned example by John Powell,the synth bass would be classified as the feature, and the percussiveelectric muted bass and double basses as the accompaniment. These twoauxiliary items do not conflict with the main bass part, and couldfeasibly be added to any such texture with a featured bass line; thefeatured bass, on the other hand, would not fit into any other texturethat has a featured bass part.

An explanation of textural classifiers now follows:

Melody

The paradox of which is hierarchically more important, melody orharmony, has been a subject of debate for centuries. The systemintelligence of the preferred embodiment takes a stance that form isgenerated through the flow and pace of chords; however, it is possibleto change the connotation of a chord, or string of chords, throughmelodic passing notes, and harmonic substitutions—both of which may bemeta-tagged as textural components.

Mostly, melodies are typically all classed as features, although somesparse melodic components can be considered accompaniment melodies: thatis, they do not counter a given melody, and are not consuming thetextural space that a featured melody would. In the event of a bassmelody, the category of the heuristics would be both tagged as melodyand bass, and as a feature. This way, there will not be a conflict oftexture in the bass region, but certain accompaniment bass componentscould still be inserted into the texture.

A textural component classified as a melody that is also tagged as afeature may well bring certain alterations to the scale or mode of thegiven texture. In the case of the exemplary The Bourne Supremacy, thereis a main melodic feature throughout the film that quite often prevalentin the celli, and revolves around a falling melodic minor scale with aflattened 2nd. This melodic component would not sit well with any othermelodic component that is using a natural 2nd, therefore it would alterthe given mode for the texture and any accompanying melody. No othermelodic feature would be able to override this because only one featuredmelodic component can be present at any given time.

Counter-Melody

This category of textural element may be linked to a melody, or simplybe a melodic element that sits around the temporal space where a melodymight sit. This applies typically to guitar riffs, melodic bridgingfeatures in orchestral textures, and melodic components that emphasismode and tonality, but do not present a strong melodic pattern.

Typically, a counter-melody can play with many others, so they aremarked as accompaniment. However, if a specific counter-melody isdesigned to work in conjunction with a melody, then this can be markedas a feature to make sure no other such textural elements that areinteracting with a melody get in the way.

Harmony

A component that is tagged as a feature for harmony states that it doessomething with a chord (as known in jazz), or a chord that featuresmultiple extensions, like a #11 chord. As with melodic components,components marked as harmonic features are marked as such because theywould be deemed to interfere with each other. The issue of how to copewith potentially clashing requests for a melody component that wishes toalter the given scale, and harmonic components that change notes withinthe given chord is discussed later.

Bass

A bass feature occupies the textural space in the bass range, with thistypical of an electric or synth bass line. Bass components that are notfeatures but which are marked as accompaniment will simply occupy thebass note of the chord.

Pitched Rhythm

This is any percussive component that is pitched, such as a trip hoploop that has tuned components that could clash with other such tunedcomponents. It also incorporates orchestral tuned percussion.

Non-Pitched Rhythm

This textural component is reserved for instruments such as shakers,timbale, HiHat patterns, etc. Examples of a feature in this space wouldbe the type of power-drum patterns one hears in many modern film scores,such as at 1:17 in Rogue One (Edwards, 2016) and throughout the cueFuneral Pyre (Crowley & Greengrass, 2004), or any other type ofprominent non-pitched feature. These rolling dynamic power-drum motifswould suffer texturally if they were interrupted by other such non-tunedfeatures.

Drums

This covers all rhythmic patterns that come from drum kits. If marked asfeatures, these are drum patterns that lie out a specific groove towhich other accompanying patterns are subservient. Non-featured drumpatterns are auxiliary components such as military drum patterns,patterns that in themselves have connotative properties, but which donot interfere with the main thrust of the groove.

With respect to tempo and time signature changes, the approach advocatedby the invention renders the timeline as invariant. Film is mapped outacross time in seconds and frames. However, embodiments within relevantaspects of the invention are arranged to alter the tempo to create moreor fewer bars on the musical ruler. Unlike other sequencer software(Cubase, Logic Pro, Pro Tools) in which tempo does not affect the timeruler, the functionality of the system intelligence evaluates, havingregard to the supplied narrative, how much musical material will fitinto a given requirement and then generates a best fit solution for thegenerative composition. The timeline can have multiple tempo changes toallow for different paces throughout a cue, and to enable the timing ofarrival at hit points.

Section B I. Generative Functionality of the Heresy GenerativeComposition System

To this point there has been a generally philosophical discussionsurrounding the ideas that underpin the generative compositional systemof the present invention.

To this point, there has been, in fact, a general explanation of thepreferred system's hierarchical workflow. We now examine this hierarchyin detail, as well as the tasks that are performed at each level toexpose the generative method of aspects of the invention.

An initial outline is now provided on the overarching principle of howthe Heresy system of the aspects of the present invention is embodiedand functions. This outline explains the hierarchy for how variouscompositional tasks—from writing chords, through to writing textures—arehandled. Secondly, the heuristic mechanism and organisational structurefor processing logical tasks is explained. Finally, detail is providedabout the preferred properties, functions and interactions between thecomponents and also the preferred steps involved with generating acomposition.

II. Heresy System Overview

FIG. 5 gives the outline for the different hierarchical layers 100within the Heresy system embodying a multiplicity of complementary butindependent inventive aspects. These layers flow from top to bottom.

Firstly, briefing elements 102-106 are requested from the user.Secondly, these elements 102-106 are interlaced with generated elements108 to create a complete set of requirements that fill the timeline ofthe piece of music that is about to be generated. From here, theheuristics of the system, as interpreted and applied by systemintelligence, will generate the chord schemes 110 on which the textureswill operate and be strung together.

This is achieved through a mechanism that makes use of “Form Atoms”.Form Atoms are a meta-chord scheme and thus the principles by andstarting point from which a coherent chord scheme is written/generatedand, ultimately, a composition is created. Each is a snippet of music(i.e., a musical section) of varying duration that has a lengthdependent upon the nature of the analysed musical expression and, assuch, each represents a building block within the generative system ofthe preferred embodiments. Each Form Atom is derived frominterpretational analysis—either manual or computer-based usingWHAT—from a library of existing independent compositions, and is storedas an indexed emotionally-described record that is accessible for futurecompositional use. Form Atoms are thus meta-chord syntacticaldescriptors. Each one has a small stored snippet of chords from apreviously analysed work, and a generative set of heuristics that, whenrun, can produce variations of snippets with similar connotativeproperties as the stored one.

The Form Atoms, such as reference numerals 120-124, include a generativeset of heuristics that, when run, produce variations of the stored chordsnippet (extracted from the earlier analysed work) to create chordschemes 128 that have a well organised form, narrative direction andpurpose. The Form Atoms are chosen and strung together through a bespokesyntax mechanism. These sequential chord schemes are then used to give atexture generator 130 the harmonic palette on which to orchestratemusic. The final output of the Heresy generative composition system ismusic 132 created from the heuristics within the texture generator.

Each Form Atom has a specific syntax internally and to each other but isself-contained in its nature, and each Form Atom embodies or possessesthe following signal properties, generative characteristic orattributes:

1. A specific set of chords in a local tonic expressed as intervaldistance relative to the local tonic having both pitch and tonality andthus a key centre for the Form Atom;2. Predicates that are formed from:(a) A form function definition based on logical operative selectionbetween musical phrasing that is one of a question, an answer or astatement and, optionally, whether the Form Atom operates as a modulatorthat permits a change from the current local tonic to a new local tonicin the next Form Atom, a modulated Form Atom which indicates thepreceding Form Atom has a different tonic, both or neither a modulatingor modulated Form Atom (meaning that the local tonic stays the samerelative to preceding and following Form Atoms) and, further optionally,whether the Form Atom appears at the beginning, end or neither thebeginning nor the end of a particular piece of music; and(b) A progression descriptor establishing the nature of cadential orsequential progression between adjacent chord atoms, i.e., the passageof the chord atom scheme across time;3. A generative set of heuristics/rules that support generation of a setof chords in a chord scheme or many different sets of chords in the sameor different tonics that achieve the same form functions and which thushave the similar associated emotional/musical connotations, andheuristics that space out temporally any number of generated chords forany given length of musical time to fill the briefing space;4. A tagged descriptive association with an emotional connotation thatarticulates one or more realistically palpable emotional response(s)experienced by a listener when the Form Atom is used in a chord schemein accordance with heuristics described herein, with such a descriptiveassociation providing relationships to music elements, e.g., chords,chord timings and chord distances to their tonic. These descriptiveassociations or “placeholders” can be taken from a library so as topresent consistency with terminology used in any narrative brief,although this is not a requirement provided association betweendifferent descriptors used in different parts of the system of theinvention can be resolved as equivalent, similar or neither in semanticspace; and5. A smallest musical phrase that makes musical sense and which has adescribable relationship with neighbouring Form Atoms; and optionally6. Metatags, such as composer name, instrumentation and/or genre asexamples amongst other more specific detail, including (for example) thename of a suite of specific preludes or a series of films. This allowsfor easier referencing to find styles in a generative phase ofcomposition when briefing considerations are identified. This listallows for further Form Atom refinement from the briefing mechanism.7. A Form Atom cannot contain a tonic in the middle of itself

Form Atoms provide harmonic structure and the ability to generateharmonic structures that obey compositionally good form, and they storea list of textural components in a classified state which define textureand which permit maintenance of textural continuity in the generativecomposition.

The system, as a whole, therefore functions to generate and store listsof Form Atoms that are linked to lists of preceding or following FormAtoms through Markov-chain associations that identify, from a corpus ofartefacts, prior transitions that have worked musically with good form.

Returning to the issue predicates and what is meant by the termsquestion, answer and statement.

A question is a chord scheme that suggests tension requiring mentalsettlement as indicated by notes that have appeared within a harmony ormelody and which are questionably present because they are outside ofthe key centre of the local tonic of the Form Atom. Multiple successivequestions can be asked musically.

An answer is the resolution of the question which operates to resolvethe presence of the questionable tones (i.e., pitch) or notes (i.e.,pitch with duration) from the mind's perspective by reinforcing the keycentre of either the local tonic or any new tonic of the answering FormAtom. An example of this are the opening two phrases of “The Love Theme”from Superman by John Williams.

A statement is entirely self-contained from a musical question anddoesn't imply or induce any meaningful musical tension that requiresrelease through resolution. A statement is neither a question nor ananswer.

Aspects of the present invention that relates to Form Atoms thus haveappreciated that all chords within a chord scheme relate to a localtonic, e.g., C or Cm for the major and minor scales of C. Moreover, thesequence of chords is less valuable than an understanding ofrelationships between chords. If you know the relationship between, sayDm and G with a local tonic of C, in terms of MIDI separations (i.e.,chord IIminor=>chord V for Dm and G) within the degree of scale, thenthis sequence of chords can be repeated in any different key centre(e.g., chord IVminor=>I in the local tonic of G).

The predicates, as indicated above, also must include (as a minimumbesides an indication of question, answer or statement treated logicallyby an exclusive OR function, XOR) either one of four cadentialprogressions (where the sequence/displacement of chords is notmathematically expressible) or two sequence progressions.

Cadential progressions take one of four alternative forms and expressways to change the tonic. Cadential progress thus can be logically XORedduring processing to identify one of:

1. a tonic that appears at the beginning (Cb) of the Form Atom;2. a tonic that appears at the end (Ce) of the Form Atom;3. a tonic that appears at both the beginning and the end (Ct) of theForm Atom; or4. the absence null appearance (Cn) of the tonic in the Form Atom.

There the two alternative sequence progressions permit termination, withthese coming in the XORed forms of

1. an interval based sequential progression, Si, where the chord isfollowed by a mathematically expressible distanced relationship withanother chord; and2. a tonality-based sequential progression, St, which relates to thescale of the local tonic and a sequence of chords which havemathematically expressible relationships that can be repeated foreverand which is based on tonality of the local tonic.

Cadential progressions therefore string together as a series of chordswith relation to the key centre of the Form Atom's tonic. The optionsfor which chords can be chosen from each other is extracted from allstored analysis of previous pieces. This is essentially a range ofchoices found using a Markov chain, but with relation to a given keycentre. A simple example of this might be that in the key of C weobserve that Dmin or F may come before G7, therefore, we can chooseeither of them as preceding chords to G7 if the tonic is C. We can thenperform a similar action to precede this chosen chord of Dmin or F.

Sequence progressions can be based on the tonality of the Form Atom'stonic, such as the second section of Bach's C Minor Prelude, bars 5 to14 (see Section D), or may ignore the tonic altogether and simplyproceed in a given interval sequence such as a cycle of 5ths or a risingsequence of major triads spaced in minor thirds.

In the case of a cadential pattern, if the tonic is present within theForm Atom, it could be said to be a pivot point from which we can arriveat and depart from one Form Atom to the next. Although a Form Atomcannot contain a tonic in the middle of itself, this does not precludethe well-known culturally accepted principle of a phrase's chord schemeculminating in a second inversion tonic—to dominant—to tonicprogression. Rather, Form Atoms therefore have their tonic appearing inone of the four ways highlighted above in the cadential progressionslist.

A consideration for cadential sequences is the ability to change key. Inthe event of a key change, if the new tonic features at the end of thechain of chords, then we simply state that it is not considered a tonicuntil the next atom. This means that modulations are created bysequences of new tonics. Unlike Form Atoms, the relationships of thesetonics are not relative to an external datum; instead, they arecategorised through emotional tags, and provide a component of theemotion-briefing mechanism. New tonics may appear at any point in apiece of music; within this mechanism, though, they will have at leastone Form Atom sequence before they can change. It is possible that thissequence could be one chord only, that of the local tonic, in which casecare must be taken in the briefing mechanism to make sure that suchchanges are not too frequent or else a series of random chords may beinappropriately produced.

In the case of sequence progressions, there are two possibilities: i)the chord scheme is related to the tonic, or ii) it is a regularsequence of chords which ignore it. In both circumstances, the sequenceneeds to be broken at some point. This is accomplished by an escapechord. Escape chords are related to the chords that immediately precedethem irrespective of the local tonic. They are used to break thesequence and establish a bridge to the next Form Atom. Consequently,escape chords typically produce a change in key centre.

Once Form Atoms have been analysed (and thus derived) from a series ofpieces of music and labelled with progression descriptors, Form Atomscan be strung together like jigsaw pieces. Any Form Atom that has thesame progression descriptor as another, can be interchangeablysubstituted. We can therefore generate a series of Form Atominter-relationships using the principle of Markov chains: therelationship between any Form Atom and the ones that precede or followit is established by looking at their progression descriptors as well asthe predicates. This is reflected in FIG. 6 which shows inter-Form Atomrelationships and a resulting Markov chain 602 having a permissiblechord scheme construction arising from identification of form-viableconcatenated Form Atoms capable of supporting the chord transition foridentified emotional connotation. For example, in a limited corpus thatgenerated the chains in FIG. 6 , chord V to either chord I or chord IVis permissible but transition to chord IIm is not because (a) there isno established path in the corpus, and (b) there is (implicitly) nocommon descriptor between the emotional connotations of chords V andIIm. In the case of FIG. 6 , there is in fact no established/recognisedrelationships to chord IIm (when appreciating that FIG. 6 is a highlysimplified view). The Form Atom transition from chord IV as adestination is shown in FIG. 6 to be from chords IIIm and V and itsonward permissible transitions to either chord I or chord V. All thesetranslations have been extracted by critical analysis of the historicalcorpus of music by automated use of music information retrieval (MIR)techniques or otherwise manually coding by a musicologist.

Consequently, if a Form Atom x has an example within the corpus of beingfollowed by a Form Atom y, then any Form Atom with the same descriptoras y can follow x. This can work in any direction temporally, so we canalso precede Form Atoms using the same technique. Finally, theweightings of any Form Atom being used are based on how many occurrenceswe find in the corpus; this provides a probability selecting and using aspecific Form Atom within a new composition.

Modulation is necessary to provide a contrast between two key centresand provide structure across time. This allows for the application ofheuristics that align with the brief to move the generative compositionalong its tonal journey. A modulator Mor that is present within a FormAtom confirms that there will be a definite transition to a new keycentre at the end of the Form Atom. If the Form Atom is a modulated,Med, Form Atom, then historical analysis has identified that, at theinstantiation of the modulate Form Atom, there has been a change in key.A modulated Form Atom therefore emphasises the emotionally significantperceptible changes in surrounding and context, such as when there is achange in pace or when a narrative of a film scene must change. Amodulator Mor and modulated Med Form Atom are therefore exclusive, i.e.,an ORed logical function.

Predicate Progression Descriptor Form Function Required Required OptionsOptions XOR XOR OR XOR Cb Question Mor Start Ce Answer Med End CtStatement Mor + Med Neither Cn Neither St S_(i)

It is possible for any given Form Atom to have multiple form tags at thesame time, except for those of question, answer and statement, wherebythe atom can only have one of these at once.

There are, consequently and potentially, 6×3×4×3=216 separate lists forpredicate combinations. The number of lists may be reduced by combininglists or otherwise ignoring one or more of the optional form functionpredicates. Each predicate list will be populated with Form Atoms that,from above, include contextual descriptors linked to their respectivecontent that define a real-life emotional experience, feeling oremotional connotation that can be tied to both a briefing narrativeinput into the system intelligence (e.g., through a user interface) and,further, to semantic descriptor(s) linked with each texture.

FIG. 7 provides an overview of the mechanism for generative compositionachieved by the various aspects and combinations of embodiments, withthe extent and depth of any combination merely varying the level ofsophistication, implementation complexity and/or attainment of thegenerative signal that is eventually output. More particularly, FIG. 7is a schematic overview of how heuristics are logically organised andprocessed.

Independent of the tasks that the heuristics perform in accordance withthe concepts of the present invention, FIG. 7 shows the affordancesnecessary for a heuristic mechanism that organises them; let us considerthese in turn:

1. There is an ordered method for how the heuristics are processed. Thisis shown in FIG. 7 by following the numbers attached to the task andthen succeeding sub-tasks.2. There is an overall percentage chance of the task being performed.This is represented by a percentage at the front of the task box.3. There is a branching mechanism for subtasks. The percentage chance ofthe sub-tasks being processed is used as a weighting mechanism for theprobability of taking each branch.4. There is a logical operator on the branching mechanism that allowsfor all or only one sub task to be processed. Depending on the logicaloperator (AND or XOR), we process either one or all of the sub tasks. InFIG. 7 , task 7 is dependent on the XOR branching from task 6, andtherefore task 7 is performed by either one of the sub-tasks attached totask 6. One of these sub-subtasks has a 25% chance of being processed,the other has a 75% chance of being processed.5. There is the ability for a task to be null, offering a branch onlyfor further subtasks; an example of this can be seen in process 6 withinFIG. 7 .

The generative compositional system of the present invention is,predominantly, a software implemented system that is based on a bespokeexpert system running code. The system, as will be understood, thereforeincludes one or more processors. This system intelligence will call oncode stored in memory, and will retrieve, manipulate and return data toand from storage, such as a database or other memory storage. Thedatabase may be local to the expert system, but equally it may beremotely located and accessible via a wide area or local area networkand appropriate network connection. Equally, the user interface may be acomputer or other client device that provides an ability to upload,download and/or stream data and media content to any logicallyappropriate part of the system for reason of storage (in one or moredatabases), manipulation and/or output (whether streamed or downloadedor imprinted) as a playable media product, including but not limited toa bespoke user-centric and/or user-selected soundtrack for aninteractive game. In short, the underlying system architecture iswell-known, although the approach to processing and generativecomposition efficiency yields manipulated audio signal data (whetheraligned with a film brief of for its own sake and purpose) that hasimproved characteristics and qualities. The system provides asignificant advance in the field of audio signal processing in thecontext of, particularly, audio composition.

Heresy's compositional output is derived from this briefing mechanismfrom which two requirements for the generative mechanism can beextracted (by, for example, NLP or more structured responses to specificquestion posed in relation to a selectively definable timeline). The tworequirements are:

1. that the mechanism can be briefed by a non-musically skilledindividual;2. that the brief can contain information on the connotations that thecommissioner desires at any given point in the composition.

To fulfil these requirements, the system and in particular the systemintelligence needs to be able to generate musical output without anyskilled musical input, whilst responding to input concerning emotionalconnotations. This is achieved through a hierarchical generativemechanism 100, in which chord schemes, textures and melodies are createdhaving regard to the briefing requirements. This mechanism isrepresented in FIG. 8 which shows the three major method steps (andinternal processing, including data management and data processing) tocreate a composition from a given brief. The steps are:

1. Generate 102 Form Atoms,

2. Generate 104 Chord Schemes—this component creates strings of chordsthat are related and fulfil briefing requirements. This is because theyare made from related Form Atoms' generative heuristics.3. Generate 106 Textures—this component generates musical material forinstruments based on the generated chord schemes and briefingrequirements.

The system performs analysis on the musical corpus (or at least aportion of it) stored in a database 110. This results in historicallystored music being broken down into Form Atoms and each classified interms of both the aforedescribed predicates (or a subset thereof) andemotional descriptors that linked to each Form Atom to reflectassociated emotional connotation of that Form Atom. The Form Atoms canhave ancillary metadata, such as genre information and composer (to nametwo exemplary categories). The analysis andclassification/categorization may be manual and conducted by amusicologist making informed parsing of the music to identify, e.g.,beginning and end points of each Form Atom as well as other propertiesand characteristics of the Form Atom (as discussed herein in terms ofpredicates), or otherwise the classification and assessment may beentirely or partially based on use of a trained AI/neural network thatcan import content meaning to extracted file properties representativeof the predicates. Such AI systems are described, for example, in US2020-0320398 “Method of Training a Neural Network to Reflect EmotionalPerception and Related System and Method for Categorizing and FindingAssociated Content” and other such patents in related AI technology.

The flow process that is within FIG. 8 indicates that the user brief 114may also influence the pieces file. To this extent, the pieces filecould simply be the entire database, although it would be a subset thatreflects requirements for a particular genre of work, e.g., jazz, or aparticular composer, e.g., Bach, and artist, e.g., Pink Floyd, to beused in the generation of the pieces file. This simply reduces thecomplexity in generating following and preceding chord trees or FormAtom trees.

Using a Markov chain approach, connections that extend both forwards andbackwards from each Form Atom, drawn into the pieces file, areestablished and mapped 112. Essentially, this tree identifies existingpermissible paths/transitions between Form Atoms in earlier analysedmusical pieces. This process is then refined in the generation ofspecific Form Atoms that align with the brief, wherein the emotionalconnotations associated with each Form Atom are resolved by the systemintelligence against briefing requirements thereby to select relevantchord atoms that are both musically emotionally relevant and germane interms of underlying musical properties. The formation of trees and,indeed, the alignment of emotional connotation between the reference inthe Form Atom and the stipulated user brief are generally reflected inFIG. 6 . In short, viable inter-relationship transitions are identifiedin the trees and these stored for use in the subsequent compositionprocess. Again, the Markov chains are associated with the requirementsof the brief, e.g., a need for raunchy heavy rock for a scene in a barthat has a stipulated start and stop time, so that relationships betweenrelevant Form Atoms align with the brief and provide compositionaloptions for transitions along the composition path.

Based on a brief 114 that is input into the system, the systemintelligence selects 116 an opening Form Atom 118 from Form Atoms 117 inthe pieces file (or more extensive database), which Form Atomcorresponds to the system-interpreted requirements of the brief.Referring again to the brief, the creation of a Form Atom string isactioned 118, which string may include blank periods that must beauto-filled to provide an end-to-end composition that does not containbreaks in audio. The process then moves onto chord scheme generation104.

In terms of a briefing tool that permits workable input, this generalrequirement for such a tool is its ability to map pace across time,i.e., a musical time ruler. Preferably, it should be adaptable throughtempo and time signature changes and sufficiently receptive to allowidentification of:

1. Hit points;2. Sustained features;3. Discourse choice;4. Chord scheme requirements, including(a) Compositional pace: chords over time, modulations, tonality shifts,(b) Emotional connotations (bass pedal, cycle of 5ths, mood tags), and(c) Form function; and5. Texture requirements.

Brief filling is a constraint satisfaction mechanism and may be achievedby a generic algorithm or on a more laboursome basis involvingconsideration and recommendation. The process of insertion of fillarises because the briefing mechanism allows for a Form Atom to bespecified at any point on the timeline through the use of a Form Atomsrequirements list. This list will more than likely contain a series ofForm Atoms that do not necessarily tessellate, leaving gaps in betweenthem. The constraint-satisfaction mechanism operates to fill in the gapsin the list, which is preferably exercised through heuristics. Thisgives a localised treatment of the most popular parameters requested forForm Atoms. The system then fills in the gaps with atoms that have theseparameters. The requirement for this system-centric correction orinterpretation is therefore dependent on the extensivity of the suppliedbrief. In-filling of gaps will typically consider and account orcompensate for:

1. the mean length and average number of chords per bar within eachtempo change in the cue.2. gaps with request parameters that have values.3. truncation of the final atom and suitable adjustment parameters toachieve fit.4. averaged chord density per bar within a given tempo section andparticularly such that chord density is set in each atom to reflect anumber closest to the average number of chords per bar within the giventempo section.

Briefed sections will typically have properties requested by the user inthe form of emotional connotations, form functions, and meta-tags. Torefine the list of options, we prioritise in the order of formfunctions, then emotional functions, then meta-tags. Firstly, if thelist contains any item or items with the required form function, weremove all other items in the list that do not have the appropriate formfunction tags. This is then repeated for emotional connotations, andfinally for meta-data. We then chose an option that satisfies thegreatest number of tags in general.

Although still at a level of abstraction, a chain of chord schemescontains all the information necessary for a harmonic map of thecomposition, including position timing between chords. From thisinformation, it is possible to create the relevant notes at any givenpoint in time, and apply them to textural elements such as harmonic andmelodic parts.

From the brief 114, the tonic is selected 120, with this providing aprimary/priority tone and available chords (with tonic pitch andtonality 1220 expressed in terms of note displacements between I and VII(and which includes minor offsets from the full notes of the degree ofthe scale). Having regard to the brief, a chord scheme is then created124 and a chord scheme train 126 stored.

Again, referring to the brief, texture generation is applied 130following extraction 132 of relevant textural group files having regardto the brief and descriptor correspondence or similarity between theemotional connotations of the Form Atoms in the assembled chord schemechains. Writing 134 of the textures chord scheme thus leads togeneration of a composition which can be sent 138 to a sequencer foreither audio broadcast or storage, as the case may be.

Returning to the issue of Form Atoms and taking a deeper look at thebenefits associated therewith, the Inventor has realised that harmoniccontext is the driving force for the choices that are madecompositionally. From this, the acceptability of any given chordfollowed by another chord is dependent on the harmonic context createdby neighbouring chords and their relationship with a common tonic, withthis manifesting itself in the mind's recognition and physicalgratification. Hierarchically, whilst chords are dependent on theirneighbours, adjacent sequences of chords also need to be self-containedentities that are related to each other. It therefore follows, followingthis revelation, that sequences can be substituted for alternative onesdepending on their common harmonic properties, such as: do they end witha recognisable cadence to the tonic, do they feature a tonic at thebeginning, or maybe at the end? Within the context of the invention,recapitulating specific chord schemes verbatim is avoided through thecreation of heuristics that can produce not only the chords for anygiven analysed sequence, but have the logic to produce differentvarieties of chord sequences of similar or differing lengths in theirplace—and whilst any rules of how the sequences connect through certainspecific chords may restrict the system's chord choices, it will ensuresound compositional flow across the sequences.

Sequences are delineated and categorised through rules with respect tothe occurrence of their tonic. Perceptually, they appear to be ofsimilar length to a musical phrase, although this may not be the case.These small sequences are the aforedescribed Form Atoms. They are thesmallest possible building block that can act as an independent sequencewhilst still making musical sense to the listener. Form Atoms havecertain properties, and Form Atoms with similar properties can besubstituted for each other. An aspect of the invention thus defines theproperties and constituent parts of a Form Atom, as well as themechanism by which Form Atoms may be combined.

If progression descriptors were to have complete free rein on thegeneration of potential chord sequences, then the result is that pieceswould start and end with progressions generated by heuristics that fitthe criteria but which come from the middle of pieces where the chordsmay be fully flowing. This would not generally make a good ending orbeginning to a piece of music that is trying to temporally deliver aself-contained narrative. Form Atoms that have a start or end tag meantheir heuristics are appropriate for such a setting.

As indicated earlier, the question and answer tags come from anotherimportant consideration: the problem of chord sequences that involvechords from outside the current local Form Atom key centre. An examplewould be the love theme from John William's score to Superman (Spengler& Donner, 1978), whereby the theme's exposition is accompanied by thefollowing chord sequence:

Eb=>F/Eb (or Eb #11 13)=>Ab/Eb=>Eb

Looking at this example, we can examine the consequences of keeping thischord scheme as a self-contained unit, or breaking it into two FormAtoms that are a question and answer. If the chord scheme is keptintact, then the information that is gleaned is as follows.

1. An Eb chord can be followed by an F/Eb chord,2. An F/Eb chord can be followed by an Ab/Eb chord,3. An Ab/Eb chord can be followed by an Eb chord, and4. This chord scheme can be substituted for any other chord scheme thatstarts and ends on the local tonic.

However, in contrast, the approach of the preferred embodiment considersthat this chord scheme is a question and answer and that means it ispossible and practicable to assimilate all of the chord information inpoints one through three above. From the inventive approach describedherein, a question phrase that has the tonic at the beginning but notthe end can be joined to an answer phrase that has the tonic at the end.This gives us the ability to break this chord sequence into smallersubstitutable pieces, and to change these pieces to introduce interest.By breaking this Superman example into two Form Atoms, this granularitywould allow for a construction of a series of Form Atoms that present{a, b, a, c}. This is indeed what the original piece does. If we extendthe example to see the next two Form Atoms, the question is repeated inthe original score, but the answer is different to create new interest:

Eb=>F/Eb=>Ab/Eb=>Eb=>Eb=>F/Eb=>Abm=>Bb7sus4

To recap, clearly this initial four bar phrase could be expressed as achord scheme that is cadential with the tonic at the beginning and end,but this would miss out on a series of opportunities for generation.This creates a rule that chords must be from the given local tonic keycentre. In the event of a chord altering a fundamental note in the givenscale, we break the Form Atom into a size that puts this new chord, orstring of chords at the end or beginning. This then gives the ability topivot at this chord to a newly implied key, or to follow back to thelocal tonic via the remaining chords in the progression. We tag thefirst Form Atom with a form function question tag, and the second withan answer tag. This classification process is significant for generativecomposition since it opens up greater opportunities for variation incompositional structure that satisfies good form.

Within the Form Atom, a preferred embodiment stores two pieces of chordinformation, namely the chord type and the chord's bass. An examplewould be Fm7/Bb. Their specific timing is irrelevant, because there maybe more or fewer chords generated by the atom's heuristics depending onthe briefing requirement. There are two reasons for storing these chordswithin the Form Atom. Firstly, for debugging the atom's chord-generationheuristics (because it is important to know what the heuristics werebased on). Secondly, so that a Chord Scheme Generator can obtain a setof chord trees of which chords precede or follow each other.

Form Atom Heuristics

There are two sets of heuristics that are used by the Form Atom.Firstly, there is a set to generate a requested number of chords.Secondly, there is a set to space out any given number of chords acrossany given time-frame. In the case of the first set, this is where onemay find heuristics, for example, that would generate a cycle of 5ths,or a sequence of rising triads a minor third apart. There are manyothers that will be understood by a musicologist, including Markovchains of chords derived from previously analysed works, secondarydominant to dominant jazz progressions such as a III-VI-II-V-Iprogression or a VI-VII-III-VI-II-V-I progression, or a series of chordsthat are separated by a single integer difference, such as a series offalling major triads that are all a major third apart. In the case ofthe second set, there may be a specific effect that is created from howthe chords are spaced. For example, in the central chord scheme to thesong “La Grange” by ZZ Top, as used in the film Armageddon (Bruckheimer& Bay, 1998), there is a clear intent to keep on the tonic for as longas possible and then to emphasise the two other chords in progression byplacing them on the third and fourth beats, respectively, of the finalbar of the phrase. This common I=>bIII=>IV Form Atom has a plethora ofalternative timings in other songs that also feature it: “Dragonfly” byZiggy Marley, “Starman” by David Bowie, or “Back In The USSR” by TheBeatles, to name but a few. All of these alternative timings havedifferent emotional connotations. This emphasises the importance ofchord-spacing heuristics, the importance of applying an appropriate andrelevant descriptor of emotional connotation to the Form Atom and theuniqueness of the timing that they bring to the personality of any givenForm Atom.

In the generation of Form Atoms, the point is made again that there aretwo sub-tasks, namely the generation of chord trees that looks atanalysed compositions to create forwards and backwards pointing FormAtom trees, and the creation of Form Atoms in which there is a selectionof a viable path of Form Atoms from the given chord trees taking intoaccount briefing requirements that affect the decision-making process.Form Atom trees are formed in terms of both forward and backwards pathsto address varying levels of input detail provided in the briefingnarrative. One tree contains options for Form Atoms that can follow theone we are generating from, whereas the other contains options for FormAtoms that can precede it. Both will typically have multiple branchesand both reflect identified musical progression in terms, for example,of whether a sequence of cadences makes sense. This is a qualitativedetermination based on a quantitative assessment.

When iterating through all Form Atoms of the analysed work, Form Atomswith identical meta-tags for form functions and progression descriptorsare placed into the same list. Each preceding and following atom fromthis one goes into the respective options list for forwards andbackwards for that list. Then, when a Form Atom is generated, a choicefrom these lists creates a neighbouring atom. This allows generation ofa meta-structure for the chord scheme of the composition that will makecoherent musical sense.

FIG. 9 shows how a single composition is parsed into a set of trees, andthe preceding and following options that can be selected for any givenatom generated from the lists. End and start form functions do notaffect the Form Atoms' listing, but all other categories are considered.Given six different progression descriptors, and three different sets ofform functions, this gives an exemplary number of 216 possible lists toreflect every combination.

Chord Schemes

Armed with a repository of Form Atoms, the generative compositionprocess moves to a phase of chord scheme generation. A chord schemes, asthe name suggests, is a grouping/concatenation of chords that are formedfrom Form Atoms having musical properties based on Predicates, asdescribed herein.

Chaining together of chord schemes provides a harmonic map for thegenerative composition. It is only possible to move to the compositionalphase once this harmonic map is in hand, in which third stage notes areactually generated and texture applied to reflect the briefingrequirements.

The requirements for each chord scheme come from a requirements list.Once we have generated a Form Atom for every item in the requirementslist, we use the heuristics of the Form Atoms in conjunction with theproperties of the requirements list to create chord schemes. A chordscheme consists of the following properties:

1. A tonic—this is the tonic for the chord scheme's local context. It isset from the previous chord scheme's new tonic property, or in the eventof this being the first chord scheme, the piece's tonic.2. A new tonic—in the event of the chord scheme modulating, this is setthe new key, and will become the next chord scheme's local tonic.3. A list of chords—this is a list of chords which are expressed throughthe following properties:(a) Pitch—this is the root of the chord.(b) Bass—this is the bass note that the chord is over.(c) Chord type—this gives a type of chord. Types are used later whencreating sets of pitches from which to choose notes. Types are definedby the analyst for the purposes of their own musical generationheuristics. Examples might include maj, min7, dom7 b9,myWeirdChordType1, myWeirdChordType2.(d) Position—each chord has a local relative position within the chordscheme that is measured from the beginning of the chord scheme whichitself is treated as an epoch. Rather than an absolute position (whichwould measure the chord's position from the beginning of the piece),this allows the chord scheme to be moved back and forth in time by theuser if requirements are moved or reordered.

Generating Chord Schemes

Having outlined the type on information that a chord scheme contains,the generation of any given chord scheme for the new composition, givena set of briefing requirements and associated Form Atoms, is acombination of the following factors:

1. Tonality and key—these are affected by the overall emotionalrequirements stipulated in the brief.2. Position—each chord scheme starts at a certain position, measured inbars.3. Length—each Form Atom has a specific length on the piece's timeline.4. Chord density—this is the number of chords within the chord scheme.5. Form Atom—this is the Form Atom associated with the requirement fromthe requirements list. This Form Atom contains the heuristic informationwe need to generate the chord scheme, and is selected based on therequirement's emotional connotations, form requirements, and meta-tags.

Referring again to FIG. 8 and its outlined process, an initial keycentre for the composition is firstly chosen. This is referred to as thetonic, but it is only relevant to the initial Form Atom. The compositionpiece is free to deviate from this key centre depending on which FormAtoms have been selected to reflect the briefing requirements. Secondly,through an iterative process through each pairing of Form Atom and itsassociated brief requirement, the system processes respectivechord-generation heuristics, followed by their chord-spacing heuristics.The chord-generation heuristics produce the number of chords that therequirement has in its associated property. The chain of chords are thenspaced by heuristics depending on how many chords there are, and theeffect that the Form Atom wants to produce from its chord spacing.

To initiate the creation of chord schemes, a key and tonality for thecomposition is selected as a start point. This is done just before thechord scheme generation. In short, the tonic note may be randomised bythe generative system. The major/minor tonality of the piece isdetermined on the basis of an overall assessment of emotionalconnotation requests in the brief, cross-referenced with analysed piecesthat most feature these emotional connotations. Therefore, the analysedcompositions that include/feature the most relevant connotationsinfluence the tonality the greatest.

Heuristics

Heuristics performed by the system are generated by analysis, such as bya musicologist although technical approaches are also alternative orcomplementary, e.g., the use of a genetic algorithm to evolve fewer moreaccurate heuristics based on fitness functions that test both Occam'sRazor (that fewer are axiomatically better) and accuracy in that theheuristics can explain more of the original artefact's note pitches,lengths and positions. These heuristics look for pattern recognition andunusualness in audio components and musical structures to generate arule that has the fewest number of rules that are able, from a givenchord, to generate at least one later chord or a succession of laterchords to reproduce the original analysed chord scheme in the originalmusical artefact. In short, the heuristic is a mathematical explanation.This is the basis on which, given a Form Atom database as a startingpoint and then a set of textures having aligned emotional connotationwhich are similar and preferably align with those linked to Form Atoms,composition can be achieved.

Any musical score can be explained by pitch, position and duration forthe notes. Other dimensional properties are also generally relevant,e.g., “volume” that relates to the loudness or softness of theperformance style which can itself take a number of forms, such asstaccato, etc. Every musical score can therefore be described orrepresented using something akin to the MIDI protocol, i.e., a series ofon-off switches over time. Indeed, in providing context for animplementing embodiment, in real terms each 8-bit MIDI envelope is tiedto a pulse, and running through a multiplicity of such pulsessequentially generates the performance of the musical score. A series ofmathematical functions realised in a Turing equivalent musicalprogramming language can, when combined, ordered and programmed withcorrect parameters, generate the original score from which thesefunctions were derived. Moreover, the same functions can generatealternatives and acceptable but different scores. For example, the rulemay need to explain how to generate a note in the bass from a chord in aspecific bar in the treble, and then for there to be selected parametersto be identified that, when applied to the rule, achieve realisationwith the original analysed musical notes in the original score.Furthermore, this rule can now be used in other contexts to generateacceptable bass notes even if given different chords. This particularrule may be assigned a suitably descriptive name, e.g., “very basic bassgeneration for triad in major key” for identification and re-usepurposes. The requirement may be, for example, looking at a chord in thetreble, we want the bass to be the same pitch but in a lower octave(closest to the bottom possible pitch of a bass guitar). The linguisticexplanation for the correct mathematical function may be “in selectingthe next bass note, look at all notes in the chord of interest andchoose the closest one of those notes (in terms of MIDI separation) tothe bass note in the previous bar. In this instance, the correctparameters may relate to the MIDI note separation distances in theoriginal chord in the treble as expressed in terms of the degree, e.g.I, III, IV.

The way in which the generative compositional system of the variousembodiments and aspects of the invention works requires heuristics to beused to create chord schemes, textures, fill-in briefing requirements,for the storage of historical information on analysed pieces, and how toplug certain heuristic files into each other. The system thereforedevelops a generic mechanism that is capable of producing an orderedprocessing of abstract tasks.

This section describes this processing and model mechanism, beforeconsidering the different primitive heuristics within the system thatallow for the creation of rhythms, pitches, stored analysis, chords, andchord spacing. Primitive heuristics give the analyst the ability toinput their analysis without having to write code.

These processing and model mechanisms allow for the ordered processingof heuristics, as well as the nesting of heuristics into groups that canbe copied and moved within the processing flow. It also offers theability to branch both conditionally and unconditionally, as well as toset the probability that certain heuristics or branches of heuristicsmay be processed. This is all achieved using the principle ofhypernodes.

Primitive heuristics give an analyst the ability to input analysiswithout having to write code, and are functionally configured to allowfor the creation of rhythms, pitches, chords and chord spacing for useor analysis as a consequence of them having predefined mathematicalfunctions in a Turing equivalent musical programming language.

Heuristics Framework—Hypernodes

A hypernode is a building block that allows for hierarchical processingand storing of heuristics. It has the following properties:

1. An ordered list of hypernodes (that supports recursive nesting).2. A logical operator to describe how the list should be processed.3. A probability—this is a number that represents the chance of thehypernode being processed.4. A name—this allows us to name the hypernodes so when listed we cankeep track of them.5. A musical element.

A set of heuristics starts off with one single hypernode. This node inturn contains a list of hypernodes that can have musical elementsattached. A musical element contains a specific heuristic, and any otherdata that needs to be stored with it. Every hypernode has a logicaloperator attached to it, either an XOR or an AND. If it is an AND, theneach hypernode in the list is processed in the list order; if theprobability of the hypernode is less than 1, then a random numbergenerator is used to assess whether the item will be processed orskipped. In the event of an XOR list, then only one hypernode isselected from the list to be processed, its likelihood depending on therelative probabilities of each item in the list.

Hypernode Processing

The type of musical element attached to the hypernode will affect howthe hypernode is processed. There are different iterative steps that theprocessor will take depending on this information. These are the typesof musical elements that exist within the generative musical compositionsystem of the present invention:

1. Drum—this is a rhythm-generating heuristic, not necessarilyassociated with drums but with all rhythm in general.2. Form Atom—this contains information about chords from repertoire thathas been analysed and input into the system. Form Atoms are used tocreate a meta-map of the chord schemes of a piece, as described indetail above.3. Heuristic—this is a catch-all for any heuristic that is notspecifically defined as a pitch-type heuristic. This includes chord andchord-spacing heuristics, as well as heuristics for filling in andcompleting the omitted parts of a given brief.4. Pitch—this is a specific type of heuristic that is associated withcreating pitch information based on a given chord scheme.5. Texture adapter—a texture adapter is specifically associated with atexture group. Texture adapters tie pitch, rhythm, and MIDI routinginformation together.6. Texture group—a texture group ties texture adapters to meta-tags thatcan be used by the user.

Whilst all of the above musical elements in a hypernode structure willbe processed for every Form Atom, the pitch heuristics will be processedfor every chord within a Form Atom's chord scheme. This means thattextures are processed only once, but pitch information associated withchord changes is processed for every chord.

Heuristic Components

A heuristic has only three elements that are stored within it: a name, adescription (so that the analyst can see what the heuristic does), and aprocedure, or method, that is run when the heuristic isinvoked/instantiated. This means that heuristics do not contain anypre-programmed data. If a heuristic needs data to be stored with it,then this is held in the musical element that contains the heuristic.However, a heuristic does not rely on data being created for it. This isbecause all other data is dynamically created and cannot be relied on tobe available at the point of processing. This may be due to branching,or statistical chance from probabilities not generating material asexpected. Therefore, a series of data maps are associated with differentheuristics. These contain any dynamically generated data that any givenheuristic may rely on to run its primary function.

The heuristic maps have the following properties:

1. Composition—the composition itself, which includes information on:(a) The requirements list—containing briefing information from the user.(b) Time signature—of the composition.(c) Chord schemes—which are attached to each Form Atom.(d) Staffs—the music information that has been created and is ready forthe sequencer.2. A spare Heresy map to provide the heuristic with an ability to sendinformation forwards in time to other heuristics, or to itself when itis processed again.3. Drum-heuristic-specific information:(a) A Black List—for drums that should not be processed if thisheuristic has been processed. This is useful to stop things likekick-drum patterns overwriting already written kick-drum patterns.(b) Drum—the drum that is being processed. Drums have a plethora ofproperties that are discussed below.(c) A processed drum list—this is a list of drums that have beenprocessed. Some of these may affect the notes that are processed for theheuristic in question.4. A list of generated pitch information—this is the chord-specificpitch information of notes that Heresy wishes to use when certain drumstrigger.5. A number representing the current Form Atom that is beingprocessed—this allows for surrounding atoms to be considered for thingslike their local tonic, and chord schemes.6. A number representing the specific chord within the given Form Atom.7. A flag list—this may be used as yes/no triggers for this and futureheuristics.

Primitive Pitch Heuristics

Having now established the mechanism by which heuristics are processedand how they pass data between each other, it is now possible toconsider the different types of primitive heuristics and how they createmusical output.

There are two different types of primitive heuristics, i.e., predefinedmathematical functions with variable parameters, associated with pitch:

1. Core heuristics—these deal specifically with pitch information andare broken down further into three sub categories:(a) Pitch generators—these generate pitch/frequency information,preferably represented in MIDI representational form.(b) Pitch transformers—these heuristics change the pitch of notes andchords, i.e., provide an offset which is an integer in a MIDI scale butnot in frequency scale where each tonic in successive octaves isfrequency doubled.(c) Pitch storers—these heuristics create storage areas in memory fornotes and Flags. These can be considered simply to be physical storagelocations for data.2. Logical Operators—these heuristics allow for conditional flow controlthrough “If Then Else” type mechanisms, as well as checking whethercertain conditions are true, such as note pitches, flags, and chordtypes being of a certain value. They can also check if note pitches arewithin a certain range. Essentially, these are branching functions forsub-routines.

Pitch-generating heuristics can gather pitch information from threedifferent sources: from a number that is abstractly stated by theanalyst; from a specific inversion position in a chord from the chordscheme; or from an idea staff. An idea staff is a named list of pitchlocations, and is set up by the analyst in a separate heuristic list inthe hypernode structure.

Whilst pitch information can be gathered from any of the three mentionedsources, all generated pitch information is stored in idea staff pitchlocations.

There are two different pitch-generator heuristics. The first is calleda note picker. This heuristic simply asks what the source note is, andwhere the destination for the note is. There is the option to randomisethe selection from the source if a chord or idea staff is selected. If arandomisation were not possible, then then the note picker would takethe exact value from identified ideas staff value at position 0 in thelist of pitch locations. However, with randomisation specified, it willtake a value from any of the notes stored in the “treble” ideas staff.These literal note values will change every time the chord changes, butthis picker will always point to this location. There is also a baroffset for notes sourced from either idea staffs or chords. This meansit is possible to obtain pitch information from neighbouring and nearbychords and ideas staffs, and from the pitch values associated with them.In this example, the bar offset is not specified, so the pitchinformation will come from the idea staff notes associated with thecurrent chord number in the chord scheme.

If the source is chosen to be a chord, then the note number would selecta value in the chord from the bass, e.g., in a major chord “1” wouldgive the major third and “2” would give the perfect fifth, “3” may givea major 7th or wrap back around to give the tonic an octave higher,depending on the chord that is generated at the time. The integer givesa literal value for whatever number is specified.

The alternative pitch-generation primitive heuristic is called a VoiceLeader. In this generative heuristic, a reference pitch is selected fromwhich to voice lead. This note to lead gives a reference to a note fromone of the predefined three sources (idea staff, chord, number). Thenote to be created is then chosen from a second reference source,typically a chord or ideas staff. The analyst can then specify if theywant the note to lead upwards, downwards, or in both directions from thefirst reference note. If they choose both, then the closest note will befound. It is possible to specify that the note should be forced tochange pitch in the event of the note appearing in the second referencechord; this is an example of another rule (of many). If the analystwishes the note not to wander too far from the initial pitch of a noteselected using this heuristic, then this can be specified as a range.This range is then stored in the data map and passed on to the heuristicthe next time it is written. If it ever attempts to generate a note outof range, it then has a record of what the initial pitch was and how tovoice lead from this value instead. This stops the voice leaderheuristic creating melodies and scales that wander off out of idiomaticrange for the instrument they are writing for.

It is important to note that the note picker and voice leader generativeheuristics are never picking prewritten notes unless their integeroption is selected. This means that the pitches that are chosen will bedependent on the harmony in the composition at the point of creation.

There are two types of storage heuristics. One creates a named ideastaff with a set number of storage positions; the other is a flag thatcan be turned on and off during the processing iteration. If the analystwishes to store any information, then they need to create idea staffs orflags to do this by way of these functions.

Branching and logical operations are achieved by a set of logicaloperator heuristics. The IfThenElse heuristic presents a set of threehypernodes. The first “if” hypernode checks for a given condition viaequality heuristics. There are four different equality heuristics. Theycan check if a specific note is of a certain pitch, or if a note iswithin a range of pitches, or whether a chord is of a certain type, orif a flag is in existence and turned on or off If the condition is met,the “then” hypernode is used; if not, the “else” hypernode is used.

Finally, the last set of primitive generative heuristics aretransformers. There are three specific ones. The first two are note andchord transposers. These are capable of transposing a note or an entirechord in pitch by a source value from one of the mentioned threesources: an abstract number, an inversion position, or from an ideastaff. The third one is an alternative retrospective voice leader. Itwill take a note in a given position with a given pitch, and it willmove it up or down by octaves until it is within an octave of adestination reference note. This is an effective way of removingcompound intervals in created pitch material.

Primitive Rhythm Heuristic—Drum

Although there are potentially many alternative mechanisms forgenerating the rhythmic qualities of melodies and textures from pitchinformation, a preferred embodiment uses a single primitive rhythmheuristic. This heuristic applies a rhythmic triggering mechanism forthe pitch values found in idea staffs created using the pitch heuristicsmentioned in the previous section.

The properties of the heuristic are stored in what is referred to as adrum. The drum information is stored in the musical element alongsidethis primitive rhythm processing heuristic. These musical elements withattached drum data sit in hypernode structures just like other musicalelements, meaning that they are processed in a hierarchical order. Thismeans that drums can potentially influence each other as to how they aretriggered through their generated and observed output. Whilst drums areindeed used to make drum patterns, their ability to trigger the pitchnotes of idea staffs means they have a much more powerful use than thatof just creating untuned percussion patterns.

The drum has a name for future reference within the context of theprocessing mechanism. This drum's name will be referred to by otherdrums in the same hypernode structure to affect their triggerprobabilities. There is a resolution that is defined for the drum. Thisin turn sets the resolution for two grids: firstly, the probabilitiesfor whether the drum will trigger or not; and secondly, the velocityvalue if the drum triggers. Each probability can have a value that canbe set between 0% and 100%; velocities have a MIDI range between 1 and127. If a note triggers, then the associated velocity is used. Thevelocities can be randomised around this value by a set range.

The probability in specific grid positions can be influenced by otherdrums that have been processed already and triggered. In this case,there are settable velocities for a note should it eventually gettriggered. These preprocessed drums may appear in one of two lists.Firstly, there is a not list of drums that negatively affects gridprobabilities. If triggered at a given position, these preprocesseddrums mean the current drum should not trigger, even if the probabilityis 100%. This is useful in circumstances such as the unidiomatictriggering of a closed Hi-Hat and an open Hi-Hat at the same time. Inthis example, an analyst may set the closed Hi-Hat to play on all quaverbeats, unless an open Hi-Hat has been triggered. The open Hi-Hat wouldbe processed first in the hypernode structure, and the closed Hi-Hatwould be processed afterwards with the open Hi-Hat in its not list.Secondly, there is an attractor list of drums that, if triggered,increases the local probability grid area of our current drum. Whetherthe attraction adds this probability number to the grid position to the“left”, “on”, or to the “right” of the triggered grid position is set inthe drum properties. This is useful if the user wishes certain notes tobe fired next to other notes. For example, in the case of semiquaversnare ghosting, an analyst may wish to increase the chance of a ghostnote occurring on a surrounding 2nd or 4th semiquaver if a kick drum orsnare drum is triggered on a neighbouring quaver. The kick drum andsnare drum may contribute 30% each to the probability of a ghosthappening, thus substantially increasing the likelihood of a trigger.

Drums have a pitch value. This pitch value can equate to a literal MIDIpitch, or a store position in an idea staff. Depending on whether theanalyst wishes the drum pitch parameter to trigger a specific MIDI noteor an idea staff pitch position's value, different rhythm adapters areused at a later stage when the rhythm and pitch heuristics are pluggedinto each other (such as needed to provided texture).

The drum can be forced to produce a set number of notes, or a range ofnotes, thus meaning that statistical flukes that result in sparse, ortoo busy, rhythmic patterns can be avoided. If the drum is only beingused as a method to attract or silence other drums through the attractorand not lists, then it can be set to mute. This means that it will nothave an output pitch of its own, but it will still be used in theprocessing mechanism.

The length of time that the given probability grid spans is set by aloop-length parameter. This way, a grid of 16 spread over four beats iseffectively semiquavers but spread over eight beats is quavers. It isalso possible to say how many times the pattern will occur, or looparound, and whether the pattern happens at the beginning or end of aForm Atom, or the beginning or end of a chord change within the FormAtom. This gives a powerful way to create intricate textures as chordsand Form Atoms change.

Finally, the triggered pitch notes are given a length in bars, beats,and fractions of a beat via associated length properties.

Textures

There has already been some considerable discussion of the structure andor effect of texture, particularly in relation to FIGS. 3 and 4 .Returning to the point made earlier on extending them again, usersachieve textures through specifying emotional connotations. Theseconnotations are, in one embodiment, checked against what is known as afile of texture groups. We will now consider how texture groups aremade. The workflow for creating a texture group file that contains thisinformation is represented in FIG. 10 . Texture descriptors willeventually be aligned with corresponding descriptors for relevant FormAtoms.

The creation of texture components is the physical output of thegenerative system of the preferred embodiment since, prior to textureoverlay, there is simply a chord scheme chain. Having considered how toclassify texture components and link them to a brief, heuristics forpitch and rhythm, and how to form a harmonic map for our compositionusing Form Atoms and assembled chord schemes, FIG. 10 provides anoverview of the processing involved to combine all this information andtechniques to understand how textures are specified, constructed,requested by the user, and realised by the system.

The workflow involved with the programming of any given analysis oftexture typically follows the following structure:

1. Create pitch data through core heuristics (explained above).2. Create rhythm data through drum heuristics (explained above).3. Create a rhythm processor to aggregate desired kits.4. Create an orchestrator to apply internal storage and external MIDImapping for rhythm processors.5. Create a texture group that attaches core files containing pitchdata, to orchestrators that contain rhythm and mapping data, through atexture adaptor.6. Attach meta-tags to the texture group.

Examining the Process Steps in More Detail:

1. The analyst (or program logic and system intelligence as the case maybe) starts by creating a set of heuristics that will create pitches thatare placed into idea staffs. These heuristics are programmed into ahypernode structure that is stored in a core file.

2. Next, the analyst creates a series of drum heuristics. Thesehypernodes are stored in a kit file.

3. It is feasible that there may be various different drums acrossdifferent kits that the analyst may wish to use in order to create adesired rhythm. Therefore, kit files are processed in what is known as akit processor. This uses a specific heuristic that allows for a kitfile, and associated kit from within that file, to be processed. Thiskit-processing heuristic sits in a processor file.

4. A map is created of where the eventual note information will go, bothin terms of the generative system's internal structure and storage, aswell as external MIDI mappings for attached VST instruments. Beforeapplying texture, the system has only created abstract snippets ofmusical material, principally in the form of Form Atoms with relatedprocessing to provide chord scheme chains. Texture overlay is whereorchestration takes place for a specific range, instrument, andplacement onto staffs at a specific point in the score. It is feasiblethat the orchestrator may wish to use various triggered notes manytimes, for different instruments (in musical terms, what we know as“doubling”). This is specified in an orchestrator file, which containshypernodes that tie together rhythm processors, with external MIDImappings, and internal staffs for storage of MIDI information.

There are two main heuristics that come into play when we create anorchestrator. Firstly, it is necessary to define where to storeinternally the information that is generated. This is achieved with astaff-creator heuristic. The staff-creator heuristic will placegenerated material onto a number of staffs. Whilst the ability to havemore than one staff is not essential, it is useful for displaying thematerial to the user in a way that differentiates this material fromother staffs, as well as when debugging the heuristics that create thematerial. The staffs that are created have name properties; a length inbars, beats, and fractions of a beat; a time signature that isappropriate for the material that will be written for it; and an offsetmeasured in bars, beats and fractions of a beat. The offset is appliedto the absolute position of any material. This way we can move pickupsat the beginning of phrases, and drum fills at the end, across theadjoining bar lines in order to make positive and negative anacruses.Secondly, a rhythm-adaptor heuristic is required to map rhythmicallygenerated material from a processor file, to staffs, and a MIDI channel,a core note, and an idea staff

As an example, the rhythm processor called “pianos”, with hypernodeprocessor called “my Bach piano right hand”, will be providing triggersfor notes that will request a pitch value from idea staff “treble” atstorage position “3”. It will take all pitches generated from the ideastaff and create MIDI notes for them on channel “11”, with an internaldestination staff for all this MIDI information that is named “Piano(right hand)”. The internal destination staff will provide anyinformation about rhythmic offset. If a pitch position is not specified,then it is assumed that the drum is requesting a literal MIDI pitch.This is how percussion patterns are created. If an ideas staff is notspecified, then it is assumed that all the pitches will have the sameMIDI and staff routing.

These orchestrators will work on any given pitch information that isgenerated in step 1 above; however, we may wish these triggers to workon pitches generated by a variety of different core files. Consequently,we now create a texture-adaptor heuristic to tie pitch data, toorchestrator data. A texture adaptor is given two components: a specificcore pitch hypernode generator from a core file, and a orchestratorhypernode from an orchestrator file. This texture-adaptor heuristic isplaced into a hypernode structure that is part of a texture group.

5. A texture group has a hypernode that contains texture adaptors andmeta-data that the analyst wishes to associate with the textureadaptor's output. This data contains the briefing components that a usermay specify and includes:

(a) Element types—these are the texture functions listed and discussedherein.(b) Texture Connotations—these are the abstract keywords that associateemotional connotation, as discussed herein.(c) Discourse Associations—this is the meta data connotations regardingcomposer and discourse discussed herein.(d) Purpose—this is to indicate whether the element components arefeatures or accompaniment.

Texture Generator

Previously, a system for inputting musical textures into the generativesystem has been described. Like the Form Atoms requirements listdescribe above, the system also has a texture requirements list. Infact, the system will only write music where there is simultaneously atexture requirement in the texture requirements list and chord schemerequirement in the Form Atom requirements list. These are required toprovide the necessary linkage between identical, semantically equivalentor semantically satisfactorily close emotional connotations that can bemusically linked from selection of Form Atoms that fit the entirety ofthe brief.

Earlier, there was described a mechanism by which any gaps in Form AtomsRequirements List was filed. In a preferred embodiment, the system isarranged, in view of a lack of relevant direction in the brief, tocontinue the current texture meta-tag requests until a new one ariseswith the arrow of time. This feeds back into the texture requirementslist so that the user can delete or change the texture as they see fitin between sections. This means they do not have to repeat texturerequirements in between points of changing texture in the brief.

To calculate textures, the generative system of the preferred embodimentcycles through all chord requirements and checks if a texturerequirement overlaps with it. If so, it processes the texturerequirement whilst using the chord scheme created for the associatedForm Atom. If the Form Atom starts early, or extends longer than thetexture, this does not matter because the processor is arranged toalready have composed material if early, and if late it will compose theremaining material onto the next cycle.

The generative system of the present invention preferably prioritisesrequests for featured texture elements (such as harmony, melody,counter-melody, etc.) over accompaniment elements. It creates a list ofall required elements that are features, then checks for all availabletexture groups that meet one of these requirements. This texture grouplist is then scored depending on how many other meta-tags the texturegroup can fulfil.

As explained, there may be multiple elements within a texture group.Whilst some of these elements may fit the brief requirement, others willnot. The texture group may also have metatags regarding connotationsattached to it that are also relevant to the brief. Scores arecumulative. To provide a selection process, the system intelligence mayscore texture elements that are not features but which are requested as+1, elements requested that are features as +2, and groups withappropriate metatags as +4. This takes into account weighting towardstexture groups that have satisfied the strictest criterion, namelyhaving a featured element that is requested by the brief. Generally, thesystem is arranged to choose the highest scored texture group,whereafter there is a temporary removal of the satisfied elements fromthe brief and repeat of the process to find the next appropriate texturegroups. This eventually fulfils all requested elements with and withoutfeatures, as well as encouraging texture groups with the correctmeta-tags for discourse and connotation.

Once we have selected appropriate textures, we perform two tasks.Firstly, we add the texture groups to a list of requirements that willbe checked and prioritised on future texture generation cycles if theirscores are matched. This way we use repeated texture ideas throughoutthe composition where possible, rather than changing texture ideas eachand every time a similar requirement is encountered. Secondly, thetexture groups that have been selected are processed by the systemintelligence.

To process the texture groups, these are added into a hypernode list forprocessing. However, before proceeding, the system creates a data mapthat contains the form requirement items for both Form Atom and texture.An index of these is recorded, with the composition also added into thedata map too. This is all the information the texture adaptors need toprocess the texture group.

Section C: Analysis Method

Earlier, the reasoning behind compositional decisions has been stated.There has also been a discussion concerning the preferred analysismethod used to create input for the framework of the system. Whilst afull analysis of a piece of music would disrupt the explanation of theconcepts on which the analysis is based, Section D below gives adetailed analysis of Bach's C minor prelude to highlight the concepts ofthe inventive approaches employed in the preferred system through acomprehensive and practical example.

This section will firstly offer an overview of the steps that are gonethrough in order to perform an analysis. It will then describe how theconcepts of entropy and redundancy are utilised, before going intodetail of how the analysis is performed through the use of examples.This chapter also offers a useful analytical tool that is part of theHeresy framework for inputting the analysis of Form Atoms from a givencomposition—known as piece annotation.

Overview of Analysis Steps

Before we consider the mechanism in-depth that will allow expression ofmeta-compositions, this section outlines the steps an analyst oranalytically-configured smart system must undertake to obtain a set ofheuristics that deliver a desired musical result and generativecomposition. In order to break any given composition down into theheuristics that the system needs to generate music, the system performsthe following tasks:

1. Form Overview—this process is used to breakdown the piece's overallchord scheme into constituent Form Atoms.

2. Form Atom Analysis—this allows categorisation of Form Atoms that havebeen identified in step one through their properties, as well as todescribe any heuristics necessary to create the chord schemes along withtheir associated chord spacer heuristics.

3. Texture Analysis—groupings of musical notes that can be explained bya self-contained set of heuristics are called textures. Texture analysisinvolves highlighting the entropy and redundancy that appears within thetexture (see “section titled Entropy and Redundancy” immediately below),as well as identification and explanation for how to generate whatDeliege (2001) calls cues.

For these three tasks, using Turing equivalent mathematical programminglanguage, a set of provided primitive heuristics, having programmableparameters, generates musical textures based on the output of chordgeneration and spatial/temporal heuristics which are logically sequencedthrough the principle of defined Form Atoms.

Entropy and Redundancy

The system and approach works on the premise of explaining the mostamount of music in a given piece with the fewest number of heuristics.This means that new concepts may require development of a new heuristic,whilst older ones are further generalised where possible. The principlesof entropy and redundancy, set out in our understanding of communicationtheory, present tools to work towards compression of the rule set.

Throughout the figures we highlight entropy and redundancy using apredefined colour scheme of red (darker tone in grey-scale printing),green (mid-tone in grey scale) and yellow (lightest tone). These colourshelp show how sets of heuristics can be reused and adapted throughoutthe analysis, and where we need to devise new ones to cope with materialwe have no explanation for. Whilst using this colouring mechanism intexture analysis, if the Form Atom analysis has patterns that canbenefit from this approach, then this colour coding technique can beapplied there too. These colours symbolise the following:

1. Green represents direct repeats of information for which there aredevised heuristics.2. Red highlights components of the analysis for which there is noexplanation and for which we have to create heuristics.3. Yellow symbolises where adaptation of already created heuristics isrequired, or otherwise a change in parameters is needed to give adifferent result.

Form Atom Analysis Introduction

This section shows how to classify Form Atoms into a limited set ofprogression descriptors depending on their chord scheme's properties (asdescribed earlier). This process results in interchangeable Form Atomsdepending on their properties.

Phillip Ball defines tonal music as that which has a priority tone(Ball, 2011), with phrases have functionality which gives the listener atemporal map based on the priority tone. The listener tries to predicthow the phrases will bring the piece back towards the priority tone,which involves the process of categorisation (Deliege, 2001).

To achieve the input of an analysed piece, the generative systemdescribed herein provides a piece annotation system. For illustrativepurposes, an example implementation of this piece annotation system isshown in FIG. 11 .

Piece Annotation

To annotate a piece, it is qualitatively broken down into progressionswith associated descriptors. This restricts interpretation to a set ofdescriptors as outlined earlier.

As will now be appreciated, Form Atoms are musical elements that sit ina hypernode structure for reasons of processing, including at least oneof manipulation and use. This gives the analyst the ability to structurethe piece's input hierarchically, allowing for branches within a pieceto be represented next to each other in a logical way. This can beuseful for visualising the relationship between Form Atoms that are indifferent places in the music, such as codas and repeats, and is usefulwhen the system and method of the various embodiments creates such FormAtom trees (as described above).

There is a chord list associated with each atom from the compositionunder analysis. Each chord has the properties of pitch, type, and bass(e.g., pitch=C, type=minor, bass=C). This string of chords gives anordered list which can be turned into a branching structure to giveoptions for different chords from, and to, other chords in a cadentialsequence. Each atom has a tonic pitch and associated tonality, such asmajor, minor, or one of the modes. This tonic is needed to give contextto the chord branches. If we expand on the previous example consideredin the explanation of the local tonic, i.e., D to G with a tonic of C,this is essentially a relationship that can be expressed eventuallywithin the system in semitones as tonic+2 to tonic+7. The mode of thetonic is relevant because it can be used when generating certainsequences of chords, as well as being an important factor in theclassification of the tonality of particular choices within a series ofbranches. For example, in the tonic of C major, we would expect to seean F major preceding a C major chord rather than the rarer F minor. Inthe parallel tonality of C minor, the expectation of the F chord'stonality is for F minor.

There are three options for progression descriptors: cadential,sequence-intervallic, or sequence-tonal. If cadential, the systemintelligence can deduce from the entered chords how to classify thedescriptor further based on the tonic's position being either at thebeginning, end, both, or neither. This gives the generative mechanismone component of the jigsaw puzzle necessary to construct future chordschemes. There are two Form Atom properties that can have multipleentries: the emotional functions and the form-function lists:

Firstly, considering the emotional function. In the F-to-C example justdiscussed, the rarer mode of the F minor chord could be interpreted andlabelled by the analyst with the emotional connotation “surprise”.Later, if a user asks for “surprise” in the brief requirements, thisForm Atom would become a potential possibility, and the atom'sheuristics would create a chord sequence which encapsulates thissurprise quality.

Secondly, the analyst adds form-function information. As previously, theform functions restrict options for interchangeability. Although wedescribed in depth the difference between statements, questions andanswers, it is a general rule that, under analysis, if a Form Atom:

1. feels like it is loopable, then it is a statement;2. feels like it is modulating, or that it can go to a different keycentre, then it is a question, and it will inevitably be followed by ananswer.

Each Form Atom now has its generative heuristics attached to it. Theseheuristics may be from previously written ones that are reused, or freshones that describe a new chord scheme generative mechanism. Theseheuristics consists of the two components, as again already describedabove. Firstly, a hypernode that contains the pitch and tonality chordsequence generator. Secondly, a chord-spacer algorithm which will spacethe chords that are generated over a given musical timeframe. In thisway, the number of chords that will be generated can remain independentof the timeframe in which they will eventually sit. This is important,because the timeframe itself may be quite changeable when film cues arelengthened and shortened.

Standard Chord Heuristics

This section describes the standard cadential heuristic andchord-spacing heuristics. These are our foundations for creatingchord-atom heuristics, and can quite often be used verbatim.

Standard Cadential Heuristic

As a starting point for all cadential sequences, given the tonicposition from the progression descriptor a standard approach can be usedfor creating chord trees from all the chords recorded in any analysedpieces (Nierhaus, 2009). To do this in the context of the invention,account must be taken of the Form Atom's local tonic to give theprogression context. If the number of chords to be generated is n, andin making sure that the tonic either does not appear or otherwiseappears anywhere except in the middle of the atom, four cadentialprogression descriptors are produced:

1. For a desired chord scheme which has the tonic at the beginning, wegenerate a chain of chords from tonic to tonic of length n+1. We thenremove the last tonic.2. For a desired chord scheme with the tonic at the end, we repeat theprocess but delete the first tonic instead.3. For a tonic-to-tonic chord scheme, we simply produce the chain ofchords of length n.4. For a chord scheme that has no tonic at the beginning or end, wecreate a chord scheme of length n+2 and delete both tonics. We alsoconfirm that there is evidence that the last chord can cadence to thefirst in the corpus of analysed pieces, e.g., Dmin=>F=>G7.

Chord-Spacer Heuristics

Chord-spacer heuristics, abbreviated CSH, spread out the availablechords into a given number of bars. The foundation heuristic call forany given CSH hypernode system is termed the CSHStandard method. Thismethod spreads out the chords depending on how many chords per bar thegiven CSH has allocated, balanced by each bar's priority for accepting anew chord. The method needs the given chord sequence, the Form Atom'stime signature, the number of bars, and an array of numbers representingthe priority of each bar for having chords placed in it. The methodfinds the highest priority bar and allocates it a chord, thus reducingthe bar's priority number by 1. This process is repeated for the numberof available chords.

The priority of chords for each bar is given to this heuristic by otherCSHs that are specific to progression descriptors. All bars' prioritiesare set to 0 to start.

CSH Cadential Tonic at Beginning and End

This CSH checks the number of chords to see if it is even. If so, itde-prioritises the first and last bar's priority to −1 each. If this isthe same bar, it will take all the chords. If there are two bars, thenthey will be treated equally. If there are more than two bars, then thisprioritisation will decrease the chance of the first and last barshaving chords. As the first and last chord are both tonics in this typeof chord scheme, this is a way of giving the tonics more musical spaceto breathe and to assert themselves over the other chords in the chordscheme.

If there are an odd number of chords, then the first or last tonic isgiven space to breathe, and the opposite tonic is given less time. Thisis achieved by randomly choosing either the first or last bar andsetting its priority to −1, and assigning the opposite end a priority of2. This encourages space in the chord placing of one of the tonic bars,but gives space to the other, thus making up for the unusual feel of anuneven number of bars. This technique for spacing chords is observed inworks by composers noted for phrases made up out of uneven numbers ofbars, such as Mahler (e.g., Andante third movement of the Symphony no.6, anacrusis to bar 3 through to bar 5, 3rd beat) and Burt Bacharach(e.g., “That's What Friends Are For”, bars 13 to 18).

CSH Cadential Tonic at the End

This creates even priorities for all bars of 0, except the last bar,which is given a priority of −1 to allow the tonic to breathe.

CSH Cadential No Tonic

This has an even number of bar priorities: all are simply set to 0.

CSH Cadential Tonic at the Beginning

This heuristic is a copy of CSH Cadential Tonic at Beginning and End,except that if the number of bars is odd, then the prioritisation is notrandom: the first bar is de-prioritised to −1 and the last bar has itspriorities increased to 2.

Actual chord spacing is then performed by a spacing heuristic that sitsbehind CSHStandard. This heuristic is termed CHS placer and places thechords on beats based on how many chords appear in the bar. This placingis represented in FIG. 12 .

From this set of limited standard heuristics, we can see the shape of apreferred chord generator of the generative system, or HCGen for short.This is a series of hypernodes that consists of a standard chord-schemegenerator, spacer, and placer hypernode. A root hypernode is created,and in it we place four items:

1. Standard Cadential Heuristic.

2. CSH progression specific heuristic for prioritising bars. This variesdepending on the progression descriptor.3. CSH standard chord-spacer heuristic.4. CSH placer heuristic.

This represents a typical hypernode structure for creating chords.

Sequential Form Atom Notation

Sequential Form Atoms can come in two varieties: interval andtonality-based (see above).

An intervallic Form Atom moves through a series of chords that involvechords from outside the key centre of the local tonic, so by definitiontheir form function is a question. Sequences need to break theirsequence, or they would go on forever; we call the first chord to varyfrom the sequence its escape chord. Escape chords are, by definition, inthe following Form Atom, and this Form Atom's form function is classedas an answer.

There is a standard intervallic template that we use to express thesequence and its escape chord. This can be seen in FIG. 13 . We statehow to obtain the beginning pitch of the sequence, and specify thetonality and any extensions that the chord may have. We then have twopossible arrows from this chord: one to a function that changes thepitch of the chord in semitones and the other to an escape chord. Thepitch function has an arrow pointing back to the chord to show the flowloop. The escape chord will have pitch, tonality, and extensioninformation.

The sequential Form Atom template of FIG. 13 lays out the pitch for theinitial chord, how the chord is altered through iterations, and theescape chord and associated relationship and properties.

A musical example of how the Intervallic Template works for Template 1can be seen below in the Section titled Form Atom 4.

Form Atom Analysis Example

In this section, by way of an example, a precise code brief is specifiedfor a section of film score from “The Quidditch Match” by John Williamsfor Harry Potter and the Philosopher's Stone (Heyman & Columbus, 2001),the score and a reduction and analysis of which is shown in FIG. 14 .

This demonstrates how we can break down the composition into appropriateForm Atoms that fit the predefined progression descriptors. Due todiffering frame rates for different movie formats, this section of musicis best found at 6:39 s of the commercial release of the soundtrack. Itconcerns the build-up of tension towards the final capture of theSnitch, which Harry Potter swallows and then spits out at bar 27. Theanalysis is high level and coding-language independent. Double bar linesdepict each Form Atom.

Form Atom 1 (Cadential): Bars 1 to 4

This Form Atom functions as a perfect cadence in the key of C minor. Dueto its initial tonic (albeit in second inversion) and final dominant Gchord, it feels clearly loopable and therefore is classified as astatement. The bass movement is worthy of future analysis with regardsto how bass movement can be generated in a scalic fashion; however, thismovement is not relevant to the immediate study of the chord scheme.

To produce this phrase we use HCGen with a cadential tonic at thebeginning bar prioritiser heuristic. The space given to the tonic, andplacement of the chords in general through this phrase in this phrase(two chords in the final bar), reflects how our standard chord spacerworks.

Form Atom 2 (cadential): bars 5 and 6

This phrase contains a tonic minor chord and an Abm which follows it.This Abm seems to pose a musical question which requires a response ifthe key centre of C minor is to be maintained. If we take this phrase inisolation and ask if it is loopable, it would not be a completelyoffensive cadence to go from the Abm to C minor; however, the Abm is notin the key centre due to the Cb. This is therefore more appropriate toclassify it as a question Form Atom. The treatment of this question inthe score is to accent these two chords with a harsh accent. This wouldwarrant an emotional connotation tag: “Chase Starts”, or maybe “PowerTutti”. These statements are clearly personal to the analyst, and reveala distinctive set of personal aesthetics with which different analystsmay argue. This is fine, so long as the analyst can challenge themselveswith the output and stand by the generative results as what they expectfrom their work. There should also be a consistent use of emotionalconnotation words. If the analyst wishes, the words can benon-emotionally descriptive, such as mode 1, to allow for the user tomake their own associations with the analyst's modes.

To produce this phrase we use HCGen with an adapted CSH cadential tonicat beginning and end. In our adapted version, we would specify that thetonic bar is prioritised and the last bar containing question chords(i.e., those not from this key centre) is de-prioritised to build theirtension through having more time on the foreign chord. This meanssetting the first bar's priority to 2 and the last's to −1.

Form Atom 3 (Cadential): Bars 7 and 8

This section would sound familiar to anyone who knows the works of JohnWilliams: it is the same diminished sequence that is repeated as abuild-up of tension in the Star Wars (Kurtz & Lucas, 1977) scores. Tothis end, and considering it has followed a question, we can expect thisto be an answer phrase. Confirming this, we can see that this iseffectively a secondary dominant to dominant progression (II to V) inthe current key of C minor. This will automatically give Heresy a linkfrom a bVI minor chord to the diminished II chord, therefore any sectionending or starting in either of these can call on the other as a link.

Likewise, these chords can be strung together within a cadentialsection.

We attach the standard HCGen to this Form Atom, selecting cadential notonic as the progression descriptor.

Form Atom 4 (Sequential): Bars 9 to 12

This is our first sequential phrase in the piece so far, its intervallictemplate can be seen in FIG. 15 , which represents a loop of sequenceForm Atom 3, with escape Form Atom 4 in The Quidditch Match. It is basedon a dominant 7 b9 chord which rises in semitones. This, by definition,is a question phrase because it requires an escape phrase to answer it,thereby bringing it to a halt. It is worth noting that this chordsection could just as easily start on any chord from within a range ofapproximately −4 to +1 semitones (Eb 7 b9 to Ab 7 b9), and still beeffective; however, the repeat of the previous phrase's G 7 b9 helps toground the beginning of the chromatic rise in this build up and give ita starting context. The previous G could of course be generateddifferently, so we would tend to say that in the heuristic we create,the start of this chord should be a repeat of the last chord in theprevious generated chord scheme associated with the previous Form Atom.

Form Atom 5 (Sequential): Bars 13 and 14

This contains the escape chord for Form Atom 4, hence this is an answerphrase. This escape phrase's chord is minor and its pitch is +5semitones from the last sequence chord. The 9 #11 13 chord in bar 14serves as the climactic point of the escape phrase. This is a usefulexample of how to build a chord function based on embellishment of ourcurrent chord. Our heuristics are labelled with the emotionalconnotation “embellishment”, which when asked for will call the chordcreation and spacing heuristics that follow.

Heuristically, we would describe this chord sequence as a number oflocal tonics. The first tonic is a plain triad, the last tonic is afully suspended chord with a #11th and 13th over the third of the chordin the bass, creating a first inversion. Any tonics in between these twopoints alter one note to adapt towards the final state. The number oftonics is dependent on the number of bars. We use two chords per baruntil the last bar where we have the final prescribed chord. If we runout of alterations but still have chord spaces to fill, we change thelatter chords in the sequence to occupy one bar rather than half a bar.

Form Atom 6 (Cadential): Bars 15 to 18

If at bar 15, Harry Potter had fallen off his broomstick and broken hisneck, we would have been happily content with the self-contained buildup that Williams has delivered so far: the escape function could resolveto an Abm chord and effectively finish the cue. However, as Harry pullsout of his steep dive and loses his adversary in the race to be the soleflyer, we are given an anticipation of success and the build up to awin.

To continue building the tension, Williams chooses to lift out of the Em#11 13 to Eb/G. This gives us a new way to resolve from an answer phrasein a way which does the opposite of conclusion. Eb is established as thenew key. Still, the piece could end here on a Lydian melody and fadecalmly to a final repeated chord of Eb. However, at bar 17, the chordscheme intensifies yet again with the arrival of the Em to 2nd inversionB chords.

This reveals a new type of sequential movement that could be extendedbeyond its current one cycle with immediate escape, namely that ofrising pairs of chords in semitones. This is shown in FIG. 16 —Form Atom6 sequential cadence from The Quidditch Match. This takes the chord fromthe last chord in the previous Form Atom and looks at its tonality,major or minor. If major, the first chord in this new bar is a minorfirst inversion 1 chord whose root is semitone higher. If minor, thenthis is a first inversion major chord of the same root. This patternthen repeats until the escape chord is needed.

The escape chord is related to a minor resolution as +7 semitones, andto the major as +8 semitones. The escape chord is in the secondinversion and is a major chord.

A standard chord spacer of cadential no tonic will give the desiredspacing.

Form Atom 7 (Sequential): Bars 19 to 22

This two-chord phrase can be interpreted as a sequence which escapesafter its first iteration. It could, however, be elongated to lengthenthe time taken throughout the build up. This pattern is represented inFIG. 17 —sequence and escape phrases 7 and 8 from The Quidditch Match.

Form Atoms 8 and 9 (Cadential): Bars 23 to 26

Form Atom 8 in bars 23 and 24 (and its repeat as Form Atom 9 in bars 25and 26), functions as an escape chord to Form Atom 7, and gives us a newtonic of Bb. It is apparent that John Williams uses second inversionchords as escape chords, with the tonality giving a distinctive flavour.This is the beginnings of gathering enough evidence to investigate amore common mechanism for predicting appropriate escape chords based onsecond inversions and the relationship to the last chord in thesequence, but we would need to see more examples of this in other worksto be sure there was a pattern.

Texture Analysis Example

We have looked at the various primitive pitch and rhythm heuristics(above, subsection titled “Primitive Pitch Heuristics”). In this sectionwe illustrate how one can create a texture using them. See in Section Dbelow a far more in-depth analysis of Bach's C Minor prelude, placedthere in order not to interrupt the discussion. We shall procedurallystep through the process outlined in the earlier subsection titled“Textures”.

For this section we shall create a generative version of the detachestring writing seen in the score in FIG. 18 . This figure shows theentropy, redundancy, and development of heuristics through the red (noteE in treble, first bar), green (all other notes except) and yellow (basenote and other notes in triad of first chord of first bar) colouringsystem.

The score in FIG. 18 is a four-bar section of detache string writingwith associated colour labels for note pitch. This would be orchestratedacross violins 1 and 2, violas, celli, and double basses doubling thecelli and sounding an octave below.

This style of writing is typical of many Hollywood thriller and spyscores such as The Bourne Supremacy (Crowley & Greengrass, 2004) andArmageddon (Bruckheimer & Bay, 1998). From an analytical perspective itis worth investigating why this technique is associated with certainsemiotics within films in which it features—so popular that it hasbecome a cliché. It is typically used to add gritty tension to actionscenes. It underpins adrenaline-fueled chases with action starts in fullswing. For this reason, it tends to be orchestrated in the lowest rangepossible for the instruments at hand, and this in itself normally meansthat the rhythmic pattern is given room in the texture to be the mainfeature, un-obfuscated by other instrumentation in this rhythm or pitcharea.

This requirement for the strings to be as low as possible gives us auseful starting point. Because the chords are closed in the violins andviolas, the pitch-depth restriction falls on the second violin. Theheuristics to do this will be created for the second violins withoutbeing based on previous heuristics, consequently the second violin'sfirst note pitch is coloured red. In this case, this means restrictingthe second note from the top of the texture to being as close to theirbottom G as possible without going below it. The first violins then playan inversion above this, and the violas play an inversion below. Both ofthe pitches for first notes for the first violin's and the viola's aredevelopments of the heuristics created for the second violin's,consequently they are coloured yellow.

The basses and celli simply are playing in unison as low as possible.They are therefore following a similar procedure to the second violin,but their lowest note is MIDI C1 (36). Consequently, they can use thesame heuristics developed for the second violin but with a differentparameter for their lowest pitch. We therefore colour their pitch yellowfor the first note. All the pitches for the rest of the notes in theexample are created using exactly the same heuristics as their firstnote pitch, hence their note heads are coloured green.

It is worth noting that if a chord appears one quaver before a chordchange, then the new chord is anticipated, or pushed, resulting in apre-emptive upbeat. This can be seen at the end of bar 1, when the chordchanges to that of bar 2 a quaver early. For this reason, we will needto calculate not only the pitches necessary for any given chord, butalso for the immediately following chord. Then, when the rhythmgenerator has created the placements for the chords, if a chord is aquaver away from a chord change, we can apply the pitch of the followingchord. This push will be calculated in the rhythm adaptor, whereby thelatter can tell if a chord change is coming in a quaver's time, and ifso, how to change selection from the current chord position's pitches tothe next chord position's pitches.

Step 1: Pitches

The hypernode structure for the pitch component of the analysis is asfollows:

Our first hypernode is an AND hypernode, which will process all elementsin the list given a probability of 100%.

1. 100%—CORE: Setup Ideas Staff

This sets up an idea staff with the name Strings with 5 pitch storagepositions for the current chord, and 5 for the next chord, giving 10positions in total. When the texture adaptor detects the presence of achord change a quaver after the current triggering, it will add 5 ontoits array position search, thus choosing the pitches for the chord tocome.

2. 100%—AND hypernode: “violin 2”

2.1 100%—CORE: Voice Leader

(a) This voice leads from a fixed number of MIDI G2 (55).(b) The direction is up and it does not have to change from the G2.(c) The chord to reference is the chord scheme in this bar.(d) The destination for the pitch data is Strings position 2.

2.2 100%—CORE: Note Picker

The next heuristic will repeat the process of the first heuristic in2.1, but will have a 1-bar offset in its chord to reference, thuschoosing a pitch from the chord to follow. However, in the event of thecurrent chord being the last chord in the chord scheme, we will not haveany data to look for. The rhythm adaptor will still look for a note inthis array position if there is a quaver triggered at the end of a FormAtom. Therefore, this is a preemptive heuristic to cope with thissituation. This simply initialises position 6 of the Strings array witha copied value from 2.

2.3 100%—CORE: Voice Leader

As mentioned, this heuristic is identical to the heuristic in 2.1, buthas a 1-bar offset in its chord to reference, thus choosing a pitch fromthe chord to follow.

3. 100%—AND hypernode: “violin 1”

3.1 100%—CORE: Voice Leader

(a) This voice leads from violin 2 upwards in our current bar to thenext note available in the chord.(b) The direction is up and it is forced to change from the violin 2reference.(c) The chord to reference is the chord scheme in this bar.(d) The destination for the pitch data is Strings position 1.

3.2 100%—CORE: Note Picker

As with the preemptive heuristic in violin 2, this initialises position5 of the Strings array with a copied value from 1.

3.3 100%—CORE: Voice Leader

This heuristic is identical to the heuristic in 3.1, but has a 1-baroffset in its chord to reference, thus choosing a pitch from thefollowing chord.

4. 100%—AND hypernode: “violas” 4.1. 100%—CORE: Voice Leader(a) This voice leads from violin 2 downwards in our current bar to thenext note available in the chord.(b) The direction is down and it is forced to change from the violin 2reference.(c) The chord to reference is the chord scheme in this bar.(d) The destination for the pitch data is Strings position 3.

4.2 100%—CORE: Note Picker

The preemptive heuristic: it initialises position 7 of the Strings arraywith a value copied from 3.

4.3. 100%—CORE: Voice Leader

This heuristic is identical to the heuristic in 4.1, but has a 1-baroffset in its chord to reference, thus choosing a pitch from thefollowing chord.

5. 100%—AND hypernode: “bass”

5.1 100%—CORE: Voice Leader

(a) This voice leads from a fixed number of MIDI C1 (36).(b) The direction is up and it is not forced to change from thereference.(c) The chord to reference is the chord scheme in this bar.(d) The destination for the pitch data is Strings position 5.

5.2 100%—CORE: Note Picker

A preemptive heuristic: it initialises position 10 of the Strings arraywith a value copied from 5.

5.3 100%—CORE: Voice Leader

This heuristic is identical to the heuristic in 5.1, but has a 1-baroffset in its chord to reference, thus choosing a pitch from thefollowing chord.

6. 100%—AND hypernode: “celli”

6.1 100%—CORE: Note Picker

This note copies the bass at position 5. (It will sound an octave higherwhen orchestrated on the celli.)

6.2 100%—CORE: Note Picker

This note copies the bass at position 10.

This will give us all the pitch information necessary to create ourtextures.

Step 2—Rhythm

Now we need to consider rhythm. There are two chords in each bar. Thefirst appears in beat 1, either on the 1st or the 2nd quaver. The secondattack point, or stab, appears either on the + of beat 2 or 4. Therhythmic hypernode in the kit's file looks like this:

1. 100%—XOR hypernode: “1 or 1+”

This node will chose between whether the first stab in the bar comes onthe first quaver of the first beat or on the second quaver of the firstbeat.

1.1 50%—AND hypernode: “1”

1.1.1 100%—DRUM: 1Violins 1

(a) This is the drum template from which we will copy all other drums.(b) Grid resolution=8. 100% chance of triggering on the first beat witha velocity of 122. Velocity is randomised by 10 (122 gives a range of117 to 127). Loop length is 4 beats. Length is one quaver. Pitch is setto position 1 (this is the position in the Strings idea staff).

1.1.2 100%—DRUM: 1Violins 2

Copy of drum Violins 1. Pitch is set to position 2.

1.1.3 100%—DRUM: 1Violas

Copy of drum Violins 1. Pitch is set to position 3.

1.1.4 100%—DRUM: 1Celli

Copy of drum Violins 1. Pitch is set to position 4.

1.1.5 100%—DRUM: 1Double Basses

Copy of drum Violins 1. Pitch is set to position 5.

1.2 50%—AND hypernode: “1+”

1.2.1 100%—DRUM: 1+Violins 1

In short, this node contains copies of all the drums in heuristic 1.1,but the probability grid is 100% on the second quaver of the bar, not onthe first. It is worth noting that the name of the drums is different(incorporating a + sign), so that the NOT and attractor lists can show adifferentiation if necessary between these similarly named drums.

1.2.2 100%—DRUM: 1+Violins 2 1.2.3 100%—DRUM: 1+Violas 1.2.4 100%—DRUM:1+Celli 1.2.5 100%—DRUM: 1+Double Basses

2. 100%—XOR hypernode: “1 or 1+”

This node will chose between whether the second stab in the bar comes on2+ or on 4+.

2.1 50%—AND hypernode: “2+”

2.1.1 100%—DRUM: 2+Violins 1

These heuristics are copies of all the drums in heuristic 1.1, but theprobability grid is 100% on 2+.

2.1.2 100%—DRUM: 2+Violins 2 2.1.3 100%—DRUM: 2+Violas 2.1.4 100%—DRUM:2+Celli 2.1.5 100%—DRUM: 2+Double Basses

2.2 50%—AND hypernode: “4+”

2.2.1 100%—DRUM: 4+Violins 1

These heuristics are copies of all the drums in heuristic 1.1, but theprobability grid is 100% on 4+.

2.2.2 100%—DRUM: 4+Violins 2 2.2.3 100%—DRUM: 4+Violas 2.2.4 100%—DRUM:4+Celli 2.2.5 100%—DRUM: 4+Double Basses

These heuristics are processed by a custom rhythm adaptor. This adaptorchecks if the next chord or end of phrase is a quaver away from anygiven triggered quaver. If so, it adds 5 to the pitch position. Thisselects the next bar's notes from the Strings idea staff.

Section D

I. Contextual analysis of Bach C minor Prelude to Generate Heuristic forthe Generative System of Embodiments and Aspects of the PresentInvention

DC.1 Abstract

The purpose of this study is to analysis the Bach prelude with a view tocreating a set of exemplary heuristics capable of reproducing theanalysed work as well as many others.

Contextually, this analysis offers a way to turn qualitative musicaldata into quantitative empirical data, and demonstrates the validity andapproach described above in terms of the treatment of chordtransposition/manipulation, chord construction and note generation.

The abstraction of the algorithms is essentially based on expertqualitative opinion. These algorithms have a multitude of parameters andcriteria which can be changed with observable results. This gives a wayto measure the effectiveness of each assertion, and to create a bank ofheuristics which give consistent musical results and work in allcontexts.

D.2 Introduction

Whilst identifying and developing a simple set of heuristics thatreproduce the piece in its entirety, these algorithmic processes areable to produce a wide variety of quality material, too.

Like any other, the application of this analytical method is subjectiveand iterative. However, its findings provide a road map for anempirically measurable set of heuristics which can be used to test thevalidity of the analysis. Through this method, a road map is identifiedto take qualitative analysis and turn it into a set of heuristics whichcan be judged quantitatively.

The piece under consideration is the first 24 bars of Bach's C minorprelude from the first book of the Well Tempered Clavier (1722). Thiscontains data for three algorithms which are obtainable from the first24 bars' data. These bars constitute the vast majority of the firstversion of the piece, after which it jumps from bar 25 to bar 35 andends with one bar of C major, totalling 27 bars (Ledbetter, 2002, p.152).

The following study is broken into four areas: three for textureheuristics and one for phrase analysis.

D.3 Analysis Method

Throughout the analysis syntactic structures and note pitches arehighlighted. The purpose is to establish what is purely entropic andredundant, as well as what is developed material. FIG. 19 shows thetypical structure of entropic, redundant and developed material in thefirst two bars, using the predefined colour scheme of red to indicate“entropic” (darkest shading, position of notes 1 to 3 in bar 1 andposition of notes in positions 2 to 4 in treble of bar 2), green toindicate “redundant” (mid-coloured shading, position of note 4 in bar 1and all remaining notes in bar 1 and bar 2 except those expresslyidentified as red or yellow) and yellow to indicate “developed”(lightest shading and first note in both treble and base in bar 2).

D.4 Form Overview

With regards to the piece in hand, (Bruhn, 1993) breaks it down intofour structural sections:

1. bars 1-4 (perfect cadence in C minor)2. bars 5-14 (modulation to Eb major)3. bars 15-18 (modulation back to C minor)4. bars 18-38 (complex, extended cadence in C)

The analysis makes use of more dynamic fluidity in the functionality ofany given section. This section shows that the piece divides into threedifferent variations of the same algorithmic process. Section 1 is thefirst variant of this process from bar 1 to bar 18. Section 2 is thesecond variant present in bars 19 and 20. Section 3 is the third variantthat lasts from bar 21 to bar 24. These sections each have a differentalgorithmic processes to produce their material and provide insight intothe structure of the Bach prelude. From a formal point of view, each ofthese sections is capable of breaking down into more modular components.

With the entirety of the generative compositional system of the presentinvention, form is elastic and dictated by refining a set of briefrequirements based on the structure of the multi-media product, such asa film, for which it is composing. Described are processes that detailhow chord sections may be lengthened and shortened through the use ofdifferent briefing requirements.

D.5 Phrase Analysis

The purpose of this phrase analysis is to define three distinct anddifferent sets of heuristics that will generate chord schemes and formpieces.

D.5.1 Phrase 1 (Cadential): Bars 1 to 4

This phrase functions as a loopable statement which emphasises the keycentre of C minor. It demonstrates that the IV dim can be used as acadence chord to the local tonic.

D.5.2 Phrase 2 (Sequence): Bars 5 to 12

Conventional analysis attributes this section to the harmonisation of afalling scale using the first inversion major chord to third inversiondominant 7th, figured bass as 6-3 to 6-4-2 (Ledbetter, 2002). It wouldbe possible to consider this as a cycle of 5ths, except that the Ab toD⁷ chords in bars 5 and 6 do not follow a strict cycle of 5ths pattern.

The following therefore applies an approach that is more thanconventional analysis can offer, namely a set of logical heuristics toexplain both the choice of major or minor harmony, and the choice ofthese chords' roots that lie outside the strict cycle of 5ths. Thisapproach is deemed necessary because this avoids the system from beingallowed just to generate any chord in an ad hoc fashion in order toharmonise melody and thus to avoid being pushed out of the realms oftonal music where there would be a loss of the priority tone or keycentre.

The evaluation does, however, need to be able to categorise specificchord schemes if new ones are generated based on compositionalprinciples described herein.

There are several readings that are possible for the chord schemebetween bars 5 and 14. They do follow an intervallic relationship in themelodic minor scale, that of rising 3 scale steps for each new chorduntil the chord scheme has returned to Ab (equivalent to a falling cycleof 5ths within the given scale). This could be interpreted as a sequencephrase, but this still does not offer a generative structure that wouldproduce the D7 chord. A more interesting reading is that of theprinciple of the tritone substitution. Known in jazz, this is where adominant 7th that is a tritone (or augmented fourth) away from adominant 7th, can be used in place of the dominant 7th. This supports atransposition from Ab=>D7=>Gm. However, if the Ab is functioning as atritone substitution to elongate the D7, then switching these chordsaround should result in the piece still sounding quite natural, as ifthere was an extended cadence to Gm. This simply is not the case andsounds awkward when played by the algorithm in tests.

The preferred reading is to use a sequence phrase method that can beapplied to any developmental section of a piece in a minor key. Bychoosing a random place within the descending melodic minor scale andthen creating a descending scale from that note, repeating every notefor a chord change. E.g.: Ab, G, G, F, F, Eb; or D, C, C, Bb, Bb, Ab,Ab. Wherever a semitone is encountered within the scale, a tritonesubstitution is made to the dominant to harmonise the pattern, andwhenever a tone is encountered a simple II V7 progression is used. Thescale is then discarded as it is only used to generate the chordsequence.

This can be expressed in the following pseudo-code:

//make an array that contains the tonic minor scale descending int[7]scale = tonic_melodic minor descending; //create a list of chords tohold all generated chords List<Chord> chordList; //randomly choose astarting position in the scale int positionInScale = random(7); //loopthis bit until you have enough chords while (notAtEscapeTime)  // if thecurrent scale note is a semitone away from the preceding note  if(scale[positionInScale] − scale[positionInScale+1] == semitone)   // dotritone to dom7   chordList.add: withPitch: scale[positionInScale],mode: major   chordList.add: withPitch: scale[positionInScale+1] + 7,mode: dom7  else   // do minor II to dom7   chordList.add: withPitch:scale[positionInScale], mode: minor   chordList.add: withPitch:scale[positionInScale+1] + 7, mode: dom7  // move on to next not indescending scale  positionInScale++ mod 8

D.5.3 Phrase 3 (Cadential): Bars 13 to 14

The phrase 2 sequence requires an escape phrase, which occurs at bars 13and 14 as a perfect cadence to the relative major, Eb. This sequence isgenerated from a scale from the relative minor. Therefore, the escapephrase can be focused on the specific key of the relative major withoutworrying about what was going on in the sequence beforehand. This makesfor some rather interesting yet viable escape relationships, such as ifthe generative mechanism were to have finished on a scale position of Din the key of C using the pseudo code above.

This would mean the last two chords in the “chordList” would be Bbm andEb7. Using the proposed escape mechanism we would get:Bbm=>Eb7=>Bb7=>Eb.

D.5.4 Phrase 4 (Cadential): Bars 15 to 16

This phrase acts as a question in the relative minor of Eb major, theoriginal key centre of C minor. This gives a way of modulating from therelative major through the use of the relative major's supertonicdom7th, which, if we were to interpret the root as Eb, could also beclassed as the relative major 9 #11 13. This chord then calls the Bb7b9(see Section D.6.2 for the reason this chord classification), which isconnected to the following answer phrase.

D.5.5 Phrase 5 (Cadential): Bars 17 to 18

This is the answer phrase to question phrase 4. It functions as acadence to the tonic minor from the supertonic diminished (see SectionD.6.2 for the reason for this chord classification).

D.5.6 Phrase 6 (Sequential): Bars 19 to 20

This phrase reveals the second set of heuristics which are an adaptationof the first. This, by definition, means that it is a self-containedsection since it acts as a build-up to the escape phrase at bar 21. Thephrase currently features a chord scheme which moves from thesubdominant minor to the second inversion tonic via a rising diminishedchord. These chords have a tonic C minor chord superimposed at the topof their voicing. There are two ways to handle this. Firstly, create twochords at this point in time and give rules for their voicings.Secondly, give the C minor notes context within the existing chords.This second approach would result in bar 19 represented as Fm7 and bar20 as F # dim; however, the use of the B on the third semiquaver makesthese chords unlikely candidates for the bars' textures. The heuristicsused to embellish the texture appear to be based on C minor and clearlypersist throughout the phrase. Therefore, the first reading of twosuperimposed chords makes more sense. This specific example of Fm and F# dim is a conventional way to arrive at a cadential six-four; however,this common invention requires explanation in the shape of heuristics.

Section 2 (D.7) considers that this two-bar phrase appears to be playingon the fact that the first two notes of the tonic triad, C and Eb here,can be extensions for many other chords that would have these as highernotes within the chord—or extensions. To create this sequence pattern ofchords we can use the following pseudo code:

cCds[ ] = array for the chord scheme; noOfChords = number of desiredchords; newChord = new chord holder; for(i = 0; i < noOfChords; i++){ if(i = 0){   newChord = findChordWith({C, Eb}, 2 , true, cCds};  }else{  if (currentChords[i−1] has one extensions below){    newChord =findChordWith({C, Eb}, 2 , true, cCds};   } if (currentChords[i−1] hastwo extensions below){    50% newChord = findChordWith({C, Eb}, 3 ,false, cCds}0;    or newChord = findChordWith({C, Eb}, 2 , true, cCds};  } if (currentChords[i−1] has three extensions below){    50% newChord= findChordWith({C, Eb}, 3 , false, cCds};    or newChord =findChordWith({C, Eb}, 2 , false, cCds};    }  }  cCds.add(newChord)  ;}

Here, findChordWith( ) is a function that returns a major or minor chordwith any number of extensions (7ths, 9ths, etc.); it can also return adiminished chord. (An Ab5 can be potentially returned in this case as anAdim.)

As with all heuristics generated through this method of analysis, thereis a core qualitative judgement made by the analyst which produces theanalyst's first attempt in attempting to define methods which cangenerate as wide a variety of musical ideas as possible whilst ensuringthey remain musically acceptable. These heuristics are therefore refinedqualitatively by the analyst passing judgement on the return of themusical ideas that the rules produce. This can be through either dryruns or actual computation. The purpose of these refinements is to pointtowards a musically acceptable result as perceived by the predefinedaudience. How the analyst decides to define the audience thereforeaffects the compositional judgement that is made. Different opinions maybe able to contextualise different verities of returned output. In thecase of this specific phrase, an analyst with in-depth experience ofjazz may perceive certain returned chords as substitutions, thereforesubconsciously giving them a viable context that a different analystwould not. It is conceivable that a good composer would be able to offera context to justify any combination of intervals, given sufficientscope to orchestrate and prepare the given chord through its surroundingsyntax. Given a large enough sample set of pieces from any particularperiod, the evolution of heuristics offers increasing insight into thedevelopment of codes and conventions from one point in musical historyto another.

In the case of this analysis, the stance taken is that the results soundidiomatic for the piece in question. This qualitative approach oflistening to the returned values and assessing them through perceptioncan offer a bulwark against criticisms such as that articulated by Ball(2011, p. 69), who suggests that “it's a common habit of musicaliconoclasts who seek ‘theoretical’ justifications for their experiments. . . to use abstract reasoning that takes no account of how music isactually heard”.

Here, Ball is referring to the auditory-cognitive processes that a mindgoes through when listening to music. The pitfalls of creating ascientific theory for music without taking into account a model of thecognitive process is highlighted by Wiggins et al., (2010, p. 237). Theyargue that, “because music, and in particular musical structure, onlyhas existence in the mind, the very notion of a scientific theory ofMusic, distinct from mind, is suspect” and “To study the thing itself[music], we need access to the implicit, or tacit, knowledge used bymusic analysts—the structures that are inferred and experienced bylisteners and other active musicians—and to the processes that buildthem”.

The exemplary study expressed herein provides a basis for definitions ofthese tacit processes, and explains the cognitive theory behind them.

In the case of this Phrase 6, we have two notes multiplied by two chordsgiving four possibilities. The two chords always feature the 3rd degreeof the scale to highlight its harmony and the point of this section isto use the lowest extensions in the chord which is building down fromthe Eb. It is therefore irrelevant for this method to return any chordwhich alters the 5th. If this were to be the case, then the 3rd and 5thwithout the root would be a chord in the list that was already usable.The alternative voicing of the root and 5th would leave an ambiguity asto the tonality of the chord in question. This is not the case in Phrase3 where extensions are sought at the top of the chord, but in thiscontext there is no other supportive evidence for voicing orvoice-leading. It would also seem unidiomatic to combine intervals whichdo not create a third relationship of some kind, such as a natural 7thto a flattened 9th. Consequently, the approach of the invention returnsextensions which are bound to allow major and minor thirds only throughthe:

(a) 7th being major or minor(b) 9th being flattened (if 7th is minor) or natural(c) 11th being natural or sharpened (if 9th is natural)(d) 13th being natural

The method also takes an array of notes which will make the topextensions of the chord it will return. It takes an integer to state howmany extensions below these notes it will include to make the chord. Ittakes a Boolean to decide whether it can use chords with fewerextensions than this integer. It accepts an array of chords in which itchecks whether the chord it has generated exists or not.

D.5.7 Phrase 7 (Sequential): Bars 21 to 24

This phrase is interpreted as two phrases repeated. The first acts as anescape phrase to sequence phrase 6 through bars 21 and 22. It would bepossible to loop these two bars, but they feel as if they requireembellishment throughout the repeat with rising extensions (as in factthe piece does in bars 23 and 24). The need to embellish a repeatedphrase is how an answer phrase is described: one that, if repeated,appears to be building to a climactic release of a cadence resolution.

This phrase is generated by creating a series of chords that are allcadences to the tonic, in a way which gives a rising melody by creatingan initial tonic-chord texture and choosing a melody note which is theclosest viable option to the top of the main texture. (This viability isbased on the note being far enough away from the main texture to becomea cue (Deliege, 2001) as is discussed later.) The subsequent choice is acadence chord to the tonic and repeat of the tonic texture whilstselecting the treble's first note of the bar to be the next availablenote above the previous bar's top note from the cadence chord's variouspossibilities. Each time there is a return to the tonic chord, the nextextension upwards for the treble's first note (in the previous cadencechord's bar) is used. This may cause the next down note of the texturefrom the top melody note to fall more than an octave away from themelody note in position 1 of the treble. However, by re-voicing thetexture to be higher the texture is brought to within the octaveboundary of the top note in the right hand at position 1. The bassfiguration stays the same unless it ends up starting on the sameinterval as the treble texture, in which case it moves one inversionhigher to offer a harmonic alternative.

This states that the texture's voicing is dependent on the melody. Thisdoes not stray from traditional thinking, in that the octave span isidiomatic for the instrument.

D.5.8 Phrase 8 (Cadential): 35 Till End

The current analysis is not concerned with the embellishment of thedominant ending for this piece. Suffice to say, the previous sequencephrase requires an escape phrase. The escape phrase in this context is atonic chord for two bars. This is in keeping with the original versionof the piece which cut to bar 35, (Ledbetter, 2002).

D.6 Section 1: Bars 1-18 D.6.1 Initial Observations

1. Evidence of a self-contained syntagm (or sign at the very least) isfrom the fact that each bar contains a complete copy of the first halfin the second half. This only changes in bar 18, where the bass moves ina downward step from C through Bb to Ab. This exception can beconsidered within its localised context later in the analysis. Furtherredundancy can be found in the fact that the last three pitches of eachsecond beat are the same as the last three note pitches of the firstbeat. On top of this, each 4th semiquaver within the first beat of eachbar is a copy of the 2nd. This, combined with the fact that each 3rd and4th beat is a copy of the first two beats, means that there is only aneed to explain the relationships between four notes in each baralgorithmically. The rest of the bar can be generated from thismaterial.

2. From the four notes in question in each bar, semiquavers 1, 2 and 5are notes of the chord for the bar (with one exception at bar 14).

3. Bass notes on the first semiquaver appear to represent a pedalthroughout most of the piece; these bass notes change in certain barsbut not others. Conventional readings put this pedal note down to achromatic note within the bar for which most analyses provides littlemore than an acknowledgment (Bruhn, 1993; Ledbetter, 2002). It would notbe appropriate to leave such a compositional statement as thisunexamined if the underlying algorithm is to be effective. Rather, it isnecessary to establish how this note stays the same, what happens tochange it and what influences the note's pitch when it does change.

4. There are non-chord notes which appear at semiquaver 3. These notesdo not necessarily fall on the scale notes for the given key of C minor.The 2nd bar demonstrates this with the E natural in the top (right)hand. In fact, it appears as the leading note for the bar's chord of Fminor. Ledbetter (2002) suggests that Bach used chapter VI of Niedt'sHandleitung zur Variation (Niedt, 1989) in order to arrive at thisfiguration.

However, Niedt's book does not offer any explanation for the note'snaturalisation. This chapter contains rules to obtain “stronger harmony”when voice leading. The second chapter states rules for the setup andsuccessful resolution of consonant and dissonant intervals, includingdefinitions of both, but these rules do not offer a set of heuristicsfor the appropriate selection of notes in a way which can be abstractedfrom the post-rationalisation of a choice which has been made. Thenature of these rules is merely suggested in Bach's writing (includinghis abilities to break them), but they do not give us an explanation forthe pitch choices of the notes in question. A system of heuristics istherefore needed to be obtained through analysis to decide how togenerate their pitches. This set of heuristics should be able to begiven parameters to alter the emotional stimulus of the music whilstmaintaining its human aesthetic properties.

5. The pattern of direction within bars of the figuration changes inplaces. In various bars Bach chooses to alter the pattern of how thefiguration works in the left hand. This requires explanation in order tocalculate when pattern alterations are needed, and which variants areappropriate.

6. Bach's implied melody falls outside of the main texture where othernotes form the figuration. Deliege (2001) explains this phenomenonthrough the principle of cue abstraction. Based on the concept ofgrouping within gestalt psychology, the mind separates these notes fromthe main texture, giving them a sense of continuation with a melodicfunction. The following considers how to reproduce this algorithmically.

D.6.2 The Texture

From point 3 in the initial observations, taking the E natural in bartwo as a local leading note to the bar's chord of F, an explanation forthe note's pitch is derived. This asserts that the note is derived fromthe dominant of the F minor chord, C major. If we consider the G whichalso appears below the E natural in this bar, this is consistent withthe C major chord. By therefore stating that all notes in this 3rdsemiquaver position in every bar are from the bar's chord's dominant ordominant 7th, an interesting pattern emerges from the rest of the barsin the piece (not including diminished chords, which we shall considerseparately). Each dominant chord is guaranteed to have a 5th degree ofthe scale. The other note is either the 3rd to give the dominant chord,or the flattened 7th to give a dominant seventh. Furthermore, this 5this always preceded and followed by the 3rd of the bar's current chord.This pattern can occur in either the bass or the treble. While this 5this harmonised by a 3rd or a 7th note from the local dominant chord ofthe bar, 3rds are preceded and followed by roots in the bar's currentchord and 7ths by 5ths. This is essentially a different way of lookingat voice leading: the main chord of the bar must feature a 3rd to giveit its mode. This observation of how the pattern works in this piece issimply stating that the 3rd always moves down to the 5th of the localdominant and back (underlined as 3-5-3 in the analysis), and likewisefor the 1st-3rd-1st and 5th-7th-5th relationships. FIG. 20 shows thebass and treble notes within the dominant chord related to the givenbar's root.

The following analysis shows a simplified version of the movement anddegrees of each note in the relevant first five semiquaver positions.The notes on the third semiquaver are in relation to the bar's localdominant. The arrows to separate chords show the hierarchical flow.Cm=>G7 means that the Cm asks for the G7. In algorithmic terms, this isactually the opposite; the G7 needs to “see” the Cm chord to know whatdominant chord it should be. This is simply to say that the G7's pitchis dependent on the Cm.

The red-coloured (darkest shade) notes show the entropic nature of thenew observed pattern. For example, in bar two, the 3-5-3 structure isnow redundant and the 1-3-1 is entropic and unrelated as a developmentto bar one's 5-7-5. This is therefore red (see C.3). Further to this, inbar three both become redundant and the b3 is a development, thereforeshown in yellow (lightest shade). In essence, we establish heuristics tocope with the initial patterns that are found. Progress through thepiece sees adaptation of the heuristics or generation of new heuristicsto cope with the new entropic material that is encountered and thematerial that cannot be explained by the heuristics as they are (at thispoint of this exemplary analysis).

Bar two contains an entropic bass note with regards to the chord's root;however, this is clearly a development of the pedal from bar one becausethe chord has changed. The notes appearing in semiquaver five are achord note below the previous note. This is redundant since this hasalready been seen in bar one. By bar two, the pitch direction arrows inthe analysis become completely redundant in nature, thus proving theapplied methodology.

Bar three is the first diminished chord out of two in the consideredsection. This chord changes the fundamental nature of how we expressinterval positions. Initially, these diminished bars appear to functionas dominants, calling a relative minor to the root note of thediminished chord in semiquaver three, instead of the major. This is notredundant, it is a new development of the original compositionalconcept, hence it is coloured yellow (lightest shade) in the diagram.Treating these diminished chords as dominants with their local dominantappearing on the third semiquaver is in keeping with the principle ofsecondary dominants.

However, classifying the fifth degree of the scale as a flattened fifth,as well as calling the sixth degree a sixth does not make any sensewhilst talking about an even-interval chord, such as a diminished chord.It would be possible to make any bar featuring a diminished chord anexception, with its own local rules, but this would lead to creating adhoc rules. This is undesirable as the new rule will simply act as asticking plaster over the troubling statistical data at hand. However,by simplifying the interpretation of note positions within chords tosimply be positions within a given array of notes, the chords can bere-expressed as arrays. Therefore, the root, third and fifth of a Cminor chord simply become [0],[1] and [2] of an array. The actual valuescontained in the array's positions are populated by a minor chordfunction which returns the pitches as in integer notation: {0,3,7}. Wecan therefore consider 6ths and 7ths as the same thing: occupants ofposition [3] of the chord array. (This also allows use of differentharmonic systems for generation based on the algorithmic processes whichdevelop from this analysis, such as quartal harmony.) Consequently, Bars1, 2 and 3 become expressed as array positions as shown in FIG. 21 .

Whilst this simplification to the rule set means that we can deal withchallenging extensions with ease by simply putting them into a givenarray position, it makes the musical interpretation of the analysis alittle too abstract and difficult. Therefore, it is better to expressthe analysis in terms of note positions within the chord, such as 3rd,5th, etc. (bearing in mind the computational array structure that thiswill eventually fit into). See FIG. 22 .

This adaptation still does not help us cope with the harmonicindependence the bass obtains through its leading note mechanism, butexamination of more diminished chords establishes a pattern. As is seenin this analysis, the bass follows its own array rather than that of themain chord. This is generally prevalent throughout many styles ofcomposition and is represented in lead sheets by using a forward-slashto denote that the chord is over a bass which may seem independent ofthe notes that appear within the chord. Consequently, this is not an adhoc rule, but simply a fact of how music is notated, if not conceived.It is feasible to imagine any note working in the bass of a diminishedchord. The initial assumption, then, is that diminished chords take thebass note of the following bar as their bass, thus creating orcontinuing a pedal.

The interpretation of bar three being an Fdim is simply that this makesthe chord fit into the pattern of having the 3rd and 5th or 5th and 7thof the dominant in the 3rd semiquaver position, albeit a minor versionof the dominant. Simply through interpreting the chord as an Fdim, thereis no need for an ad hoc rule to cope with the 2nd, 3rd and 4thsemiquaver notes. If the chord scheme is played without a pedal bass buta root bass, conventional reading would make this note a B or G in thisbar. However, the chosen reinterpretation of Fdim would make the bass anF. This sounds perfectly acceptable. This is a simple example ofcomputational analysis pointing towards a reinterpretation of the scorefor no other reason than to simplify the model without cost to theintricacies within the data.

With reference to FIG. 23 , Bar four starts with a repeat of the melodynote in bar one. The repeat of this pitch is the first time that arepeat of a melody note is seen in the composition. We shall considerthis new, and consequently entropic, concept as more evidence for howthe melody flows becomes apparent throughout the analysis.

Bar 4 gives us our first alteration to the figuration pattern seen inthe first three bars. In practical terms, this is simply because thechosen interval jump from the 1st to 2nd semiquaver in the bass meansthat if the downward pattern continued then the bass note at semiquaver1 would be repeated in semiquaver position 5. The requirement for thisnote to rise is therefore a development of the material at hand andcoloured yellow. This happens in 10 out of the 24 bars analysed. Thetable in FIG. 24 shows the fifth semiquaver in the bass and the chordcomponent on which it lands. There appears to be no correlation betweenthe chords' local dominant 5th (in semiquavers position 3) being in thebass or treble and the upward or downward movement of the 5th basssemiquaver.

The pattern goes up in the bars listed below for the following reasons:

4: To avoid repeating the 1st semiquaver.10: To make sure the 7th in the bass is not confused as having a voiceleading relationship with the 1st semiquaver leading to a new cue(Deliege, 2001) being identified by the ear through the scale steposcillation of these two notes.11: There is no reason except for the fact that the preceding andfollowing bars change the movement pattern. This is a choice from Bachand entropic with regards to heuristic considerations.12: To avoid repeating the 1st semiquaver.14: To avoid repeating the 1st semiquaver, (this is a hint at a newmethod of producing notes at this position which will be consideredlater).17: Similar to bar 10, there would be only a scale step between the 1stand 5th semiquavers and this could lead to a bass melody beinginterpreted by the listener.19: To avoid repeating the 1st semiquaver.21: Generated by the bar 14 method, which produces such notes at thisposition.23: Generated by the bar 14 method.24: Generated by the bar 14 method.

A simple heuristic can thus be derived that produces the note atsemiquaver 5 without a pattern change and then checks to see whether itis within a tone of the bass note at semiquaver 1. If it is, then thepattern change triggers. The only exception to this is the aestheticchoice that Bach makes at bar 11.

Bar six raises the question of whether the dominant 7th D chord issimply a dominant to preserve the bass pedal. Ledbetter (2002) describesthe first inversion major chord to third inversion dominant 7th(figured: 6-3 to 6-4-2) in this piece as a standard way of harmonising adescending scale. The reason why this question is important here is toascertain whether the chord is created due to the bass movement, orwhether the pedal is created due to the choice of chords. We currentlychoose to read this as the chords creating the bass, because thissimplifies the heuristics. The bass note now falls within the chosen orgenerated chord, rather than the chord being generated ad hoc from thedescending bass scale.

With reference to FIG. 25 , Bars 7, 8 and 9 offer no new informationapart from the melody in semiquaver 1, so much so that it is interestingto note that bars 8 and 9 are complete (yet transposed) copies of bars 6and 7. This is an important aesthetic observation because the heuristicswe define will be capable of creating multiple different versions andvoicings in such circumstances. It is important to note how Bach usescomplete redundancy, repeating his voicing and textural decisions togive form to the listener's temporal predictions.

There are two possible readings of bar 11: that of an Eb chord or a Cm7chord. Minor 7th chords are indeed prevalent throughout Bach's work,(such as in the 3rd beat of the 22nd Prelude in this suite in Bb minor).By using the Cm7 version, we do not need to encounter a 1-3-1relationship in the bass in the first section's heuristics, but just thepredictable 3-5-3 and 5-7-5 relationships. However, minor 7th chords donot feature in this piece's discourse because they simply do not appearas the main chord in any other bar. If the deciphered heuristics whichare generated from this analysis are fed versions of this piece's chordscheme with both a Cm7 and Eb chord in this bar, then the voicings andarrangements played by the Eb chord sound far more natural andappropriate. We therefore choose to read this bar as version 11b foralgorithmic reasons but appreciate that it is actually version 11a. Intruth, this simplifies the preferred construction of the heuristicswhilst enabling the feed of the Eb chord into the chord scheme. The onlyconsequence is that this specific bar's voicing will not be possible.This could be developed in any later versions of the heuristics as morepatterns are discovered and better generalisations are made, but isirrelevant to the extent that this analysis proves the underlyingapproach to analysis and generative composition based on the methodologydescribed herein.

As previously mentioned, there is no functional requirement for the bassin semiquaver position 5 to rise in bar 11. This decision by Bachremains an entropic problem during the certain stages.

With reference to FIG. 27 , Bar 12 splits the mind's interpretationbetween a Cmb6 chord and an Abmaj7/C chord. If we consider this to be anAbmaj7/C pattern, then the 3-5-3 relationship breaks down for the firsttime to give 7-5-7 in the treble and 5-3-5 in the bass. If we call thischord Cmb6, then the initial b6 in the right hand can be accommodated bytreating it as a 4th element in an array, just like a 7th. However, theb6 in the bass in semiquaver 5 makes the jump through the available 5th(as we go from the 3rd in semiquaver 4 to b6 in semiquaver 5), which isproblematic considering we do not see this behaviour in the rest of thepiece. In other versions of the pattern break that make the bass in thisposition rise instead of fall in order to avoid creating a salient cuein the bass, we see the arpeggio at semiquaver 5 feature the next notefrom the bar's chord that is above semiquaver 4. Here it climbs from the[2] array position through to the [4]. This ambiguity is clearly desiredby Bach as we sense the repeated b6 jumping out as if it were a cue.This creates an effect that sounds like the piece's rhythm hasdouble-timed in this specific bar. This need for a new audible cue couldbe handled as a specific case which arises at the point of a modulation:at this point, the movement towards Eb in bar 14. This seems acceptablein regards to the important position of this pivot chord, but does meanthat the algorithm will have to be sensitive to points of modulation.This bar also resets the bass pedal back to the tonic through the jumpof a perfect fourth. This is entropic considering the bass's fallingmovement in the piece so far.

Bar 14 introduces a completely new idea in the bass by moving stepwiseup to the fourth degree of the bar's chord. This is completely out ofcharacter with the piece so far, which uses intervals from the givenchord in this position, and hints at the algorithm which develops inlater sections of the piece.

If this chord had a Bb instead of the Ab on semiquaver 5, there would beno entropy here.

As an aside, it is worth noting that the score version from which wetake modern interpretations of this piece is known as TheWagner-Volkmann Autograph. This copy was made in 1732, ten years afterthe pieces were composed in 1722. The original manuscript is believed tobe lost, leaving this as the only known copy of the first manuscript inBach's own handwriting (Palmer, 1994). However, Bach's son WilhelmFriedemann made a copy of the earliest forms of the first 11 preludeswith various small corrections made by Bach's hand, a version known asThe Clavier-Buchlein version. Owned by Yale University, this versionclearly shows that Bach initially had the Bb instead of the Ab at this5th semiquaver position. This can be seen in FIG. 28 .

The above suggests that Bach changed the note at this point in the pieceon a later revision to reflect the processes that he employs later on inthe piece. (These processes simply use the sub-dominant in position 5 ina similar way that the dominant is used in position 3.) Heuristically,this means we can separate this specific Ab occurrence from the firstsection under analysis, and consider it using the heuristics that weobtain from phrase 3 in which this figuration becomes more prevalent.

With reference to FIG. 29 , Bar 16 introduces an interesting dilemma forthe 3-5-3 relationship. If this bar is interpreted as a Ddim chord, thenthe C and Eb in position 3 bear no relevance to the dominant A of D.

Despite the Bb not actually appearing in the bar at all, the C and Ebleave only two possibilities if the 3-5-3 relationship is to bemaintained: the dominant must be either F7 or Ab. Ab makes no musicalsense because it would imply the bar is the chord of db. F7 sustains thepattern of the 3-5-3 whilst making musical sense as the dominant toBb7b9. The Bb chord functions perfectly within the chord scheme bylinking to the F7 in the previous bar. (Audibly, this bar and the nextremain highly chromatic.) Although we could use the lack of a 1st degreein bar 16 to suggest that the first array position could hold the b9, itis more consistent to expand the array to incorporate a 5th positionwhich contains the b9.

Bar 17 contains the second diminished chord that we have experiencedwithin the piece so far, (accepting bar 17's reading). The 3 5 3relationship points to yet another secondary dominant (minor dominant)at semiquaver 3, as experienced in the first diminished chord of bar 3.This conventionally would signify a dominant function for the diminishedchord. The only relationship we can see this bass note has in the piecesis that of the bass note in the next bar. This does however lead to asimple heuristic with regards to diminished chords: that they containthe bass note of the following bar's chord.

With reference to FIG. 30 , Bar 18 contains movement in the bass whichis noted in the Autograph, Kirnberger, Gerber and Walther manuscripts(Palmer, 1994). Only the Kroll edition leaves this Bb note as a C(Ledbetter, 2002). Originally believed to be a copying error, this haslater been poorly justified in the name of consistency. This is clearlya cue that is being established by Bach to end the section and emphasizethe move to F minor in bar 19. This chord ends the section in question.

This linking movement in the bass will be ignored with regards to thecurrent heuristics, which we will develop for bars 1-18, due to a lackof examples for how this cue is utilised. Any heuristic to create the Bbat semiquaver 9 would be an ad hoc rule without further supportingevidence. The 4th degree of the scale in the bass at semiquaver 5 isfurther evidence of the shift towards the algorithmic processes of thefollowing sections, just as in bar 14. Further evidence to confuse anyinterpretation is that this F at semiquaver 5 is written as a repeated Cin the Clavier-Buchlein version, thus emphasising the cue which isoccurring in the bass movement.

D.6.3 Heuristics for Section 1: Bars 1 to 18

The following commentary numbers the notes in the bass and treble byarray positions [0] to [15] to signify the 16 semiquaver positionswithin the bar.

D.6.3.1 H1.0: Calculate Bass at [0]

The pedal note: the entropic nature of the notes in the bass in eachbar's first position means we need a generative heuristic to createthese possibilities. By looking at the availability of the current pedalnote within the bar's chord and the pitch value that the note takes, itis possible to calculate this bass by checking if the bass note of theprevious bar falls within the current bar's chord. If the note does not,the next closest available note is selected from the chord which isbelow or above the previous bar's bass note. (This direction in pitch,be it up or down, is arbitrary and means we can initialise it fromconnotation requests through briefing elements processed by anoverseeing form generator.) There is an exception for diminished chordswhich are used to end sections: they simply use the note in the bass ofthe bar to which they are cadencing. This means that there needs to betwo passes whilst creating the piece. The first pass is to establish thebass notes as described without the diminished clause. The second passis to then change the diminished chords' bass notes to look at that ofthe following bar, rather than that of the one preceding them. Withoutthis double pass, the heuristic would have a null pointer when itreached a diminished chord.

This pattern continues until the bass is over half an octave from itsorigin. In this piece's case, the tonic C is the origin, meaning thatthe F # which is 6 semitones below this C is the reset position. When abass note is generated that falls below this, the pattern is reset andthe nearest note within the current chord to the initial starting bassnote on the tonic is used. This can be seen when at bar 12 the notejumps from bar 11's bass of G to the original tonic of C. In the pieceat hand, the pedal switches; rather than always falling, it chooses theclosest note that is either higher or lower. From bar 6 to 7 it fallsfrom C to Bb, whereas from bar 12 to 13 it rises from C to D.

D.6.3.2 H1.1: Calculate Bass at [1] There are 13 cases out of 18 wherethis note is the 3rd of the chord; if not then it is the 5th of thechord. For variety's sake during the initial investigation of howheuristics sound, (before we introduce overriding aesthetic heuristicswhich manage choices), we can simply make this a 50/50 scenario. Thismakes the heuristic simple: make bass [1] randomly the 3rd or 5th abovethe bass in [0].

D.6.3.3 H1.2: Calculate Bass at [2]

If the bass hand note at [1] is the 5th, then make this the 7th of thedominant 7th. If this is not the case, then bass [1] must be the 3rd: wetherefore make [2] the 5th of the dominant.

Either way, we transpose [2] below the bass at [1].

D.6.3.4 H1.3: Calculate Bass at [4]

As shown in the explanation for FIG. 24 , this note attempts to be thechord position below the value in [3] (which is a copy of [1]) unless itcomes within a tone of the value at position [0] and risks making a cuein the bass. In this event it rises to the next available chordposition.

D.6.3.5 H1.4: Calculate Treble at [1]

If the bass at [1] is the 5th, then treble [1] equals the 3rd chord notin a voicing that puts it above the bass's 5th at position [1].

Else there is a 50/50 chance that this is the root, or 1st, above thebass.

Else this is the 5th.

If it is the fifth, then we check to see if it is possible to transposethis value up an octave from its current pitch as seen in bars 4, 10, 11and 12. If the previous bar's treble at [1] is a tone or less away fromthe new value at the current bar's treble [1], then we perform thetransposition up an octave from its current pitch. (This is a simple andinitial voice-leading ad hoc rule which will need a more universal andthorough refactoring when aesthetic heuristics are introduced later.)

D.6.3.6 H1.5: Calculate Treble at [2]

If the treble at [1] is the 1st and the chord is diminished, then makethis the minor 3rd of the local dominant.

Else if the treble at [1] is the 1st and the chord is not diminished,then make this the 3rd of the local dominant.

Else if the treble at [1] is the 3rd, then make this the 5th of thelocal dominant.

Else if the treble at [1] is the 5th, then make this the 7th of thelocal dominant 7th.

D.6.3.7 H1.6: Calculate Treble at [4]

We make this the next extension in the chord below the value in treble[1]. If this value is equal to or below bass [4], then get the nextextension above bass [4]. This is to avoid crossing counterpoint lines,with which the ear copes poorly. This is something that Bach issensitive to as pointed out by Ball (2011, p. 148) with an example fromthe E major Prelude in Book 2 of the Well Tempered Clavier. This showshow Bach avoids the sonic equivalent of a Gestalt-style continuation, bymaking sure the voices do not cross paths.

D.6.3.8 H1.7: Calculate Treble at [0]

The melody note is never more than an octave above the lowest note inthe bar's treble, nor is it equal to or below the last note in theprevious bar (which is the same as treble [1] in the previous bar).Consequently, we choose a random note from the available notes in thebar's chord which meets both requirements.

D.6.3.9 H1.8: Copy the Bass and Treble to Fill Positions

The values at positions [3], [5] and [7] equal the values in [1].

The values at positions [6] equal the values in [2].

The second half of the bar is a copy of the first.

D.6.3.10 Unexplained Entropic Considerations

The score in FIG. 31 shows the different heuristics in action throughthe use of colour coding. In grayscale, however, to identify eachheuristic, the notation H # (H1, H2, H3, H4, H5, H6, H7, H8 or H9)appears above or below each note. Solid arrows are pointers to othernotes which provide information for the final pitch of the note inquestion. Dashed arrows show pointers to notes whose values are assessedbut not used due to heuristic considerations.

This final overview gives a clear impression of the hierarchy of thesection in hand. Nearly all notes flow return to the initial bass notein bar 1. The melody at each treble position [0] builds on the previousbar, trying to distinguish themselves from the value at treble position[15], with their options restricted to the range of notes an octaveabove the lowest note in their current bar. We can see the bass note thediminished chords created on the first pass before overwriting it on thesecond: the first pass's arrows are dashed and the second are solid.This visualisation shows exactly how the entropic red (darker shading)content cannot be linked to the currently understood hierarchy. This iswhere the heuristics currently break down.

The two main points where this is a serious issue are in bar 14, wherethe heuristics would choose a Bb over the published Ab at position [4]in the bass, and bar 18 where the special case bass pattern occurs—theonly point in the piece where the first and second halves of the barcontain different material. All three of these notes are notably theonly three which are different in the Clavier-Buchlein version comparedto the autograph copy from which we have our modern editions. As well asthese two salient points in the score, on a lesser scale the currentheuristics do not account for the voicing of 5-3-5 in bar 12 if we usethe Ab/C version of the chord, the only point of possible breakdown ofthe 3-5-3 pattern.

Similarly, we are incapable of producing the double position jump atbass position [5] if we express this bar as Cmb6. Apart from thesecases, the entropic components mainly highlight a lack of aestheticjudgement in the decision-making processes of the heuristics. The risingbass at semiquaver 5 in bar 11 cannot be created without an overridingaesthetic heuristic which looks at decisions made in the surroundingbars. In both of these more trivial cases, if we randomise the firing ofheuristics which are capable of producing these values, then both becomepossible. However, it does not seem sensible to do so simply because ofthe 1 in 25 times these examples occur.

Voice leading in the melody may similarly require aesthetic heuristics.A lack of repeatability in decisions from one bar to the next makes theoutput unnecessarily over-entropic for human listening. This is afurther example of a lack of purely aesthetic decision-makingheuristics. Such heuristics would simply repeat decisions in a morepredictable pattern, such as in groups of two bars, but this wouldrestrict the current system's output possibilities.

D.7 Section 2: Bars 19-20

The following two sections are based on developing the core texture ofthe tonic minor figuration.

In Section 2, Bach achieves this by inverting the initial semiquaver inthe treble to appear below the treble and bass figurations in the otherpositions but [0], sitting with the bass note as a distinctive chord andsalient cue. The choices Bach has made by using an Fm7 to F # diminishedare recognisable as a common preparation for a cadential 6 4. However,we need to express how to choose such selections algorithmically and ina way which gives enough scope for a variety of generative results. Thequestion, therefore, is what note pairings can sit below such a textureand add to it in an interesting way? Can the notes be random and stillgive a sense of harmonic movement towards, or around, the tonic of bar21? Simple keyboard experiments show that this is not the case. The useof random intervals makes no harmonic sense (unless it is a conventionalharmonic fluke). However, the use of any chord which has C and Eb in thetop of the texture does, such as an Ab chord followed by an F7 chord.

Taking the C and Eb as the top extensions, it is possible to build avariety of chords below C minor which can incorporate these two notes atthe top of the chord for the texture in Sections 2 and 3. The score ofFIG. 32 shows the possible combinations of major and minor thirds whichproduce chords in descending order of pitch.

Notably, the score in FIG. 32 shows all possible combinations (spanningan octave) of major and minor triads with C and Eb as the topextensions. Rules exclude certain bars: red X chords are unavailablethrough D5.6 pseudo code, purple X chords are excluded due to texturelimitations.

A good question to ask at this point is why the chords are triadic inform? Why not incorporate 4ths or 5ths to create chords such as thesecond inversion C minor chord we are moving towards at bar 21? Many ofthese combinations produce either the chords we have already given, orchords which make no conventional sense. Adding 4ths below many of thechords above simply produces a different inversion of the given chord.Likewise, incorporating 5ths, in other words removing certain notes tomake holes in the chord voicing, either misses out a major and minorthird to produce a more harmonically bare voicing, or producesdissonance due to a clash between a perfect fifth and any chord made oftwo major, or two minor thirds. An example of this would be adding a B aperfect fifth below an F # diminished chord. In essence, the diatonicscale, which the “7 from 12” system of western harmony has currentlyevolved into precludes use of the more obtuse chords which can be madefrom random choices of major and minor thirds. This is before we evenconsider introducing 4ths and 5ths, which exponentially increases thechord's abstractness, or simply ratify the chord we have already hitupon with the incorporated thirds through luck. It would seem that anyof the chords in the score of FIG. 32 which fit within the diatonicscale make sense. Although the E augmented chord (E #5 maj7) could beconsidered an altered chord based on the Locrian natural minor mode(Levine, 1995, p. 70), the top Eb (or major 7th) does not appear in themode, so consequently this chord does not sound like a viable option.Neither do the more obscure db augmented chords, as we are too close toobscuring the sound of a C minor components with the db chord below it.

Balzano (1980) has previously shown that the diatonic system offers aunique number of every type of interval within the scale. The intervalrelationships cannot be mapped through direct transposition; however,the brain seems to realise this, and this is the trick that Bach seemsto be using in Section 2. This method of finding chords throughextensions is then inverted for Section 3, whereby the initial chordseems to embellish upwards from the pedal G. The pseudo code within thephrase analysis (Section D.5.6) offers a viable way of selectingappropriate chords from the array of possibilities. Given this approach,we can eliminate certain chords as highlighted in red in the score ofFIG. 32 . If we consider the available space for this new cognitive cueto exist in, then we are offered limited possibilities for these cues'placement, as shown through the two alternative voicings of the C and Ebtexture in the keyboard representation of FIG. 33 , which shows possiblenotes within the textures of bars 19 and 20.

In all cases, the cue notes must appear at least a minor third away fromany other notes within the main texture or a melodic cue is established.If the semiquavers at position [4] travel outwards from the main texture(treble rising and bass falling), then we are given maximum availabilityfor the treble notes at positions [0] and [8]. However, the notes in thebass cannot repeat the pitch of treble position [0], nor fall more thanan octave below the pitch of the highest note in the bass throughout therest of the figuration (the final requirement being a stylisticobservation of the range of voicings throughout the given piece). Thisgives a trade-off in the bass: if the pitch rises at position [4], thenthere is more room for the bass but less for the treble.

This dilemma reveals one of the first cases of iterative recompositionthat the system must employ. If a desired chord scheme is required, thenthe chord texture may have to be rewritten to incorporate it. Ifrewriting the chord texture cannot accommodate the desired chord scheme,then the chord scheme must be rewritten. This iterative process ofnegotiation offers a potentially descriptive insight into thecompositional process. For the given example's textures, the chords inthe score of FIG. 32 that are not available are crossed out in purple.

This leaves six possible chords which can all be used in a random order(excluding the F # dim which can only be 2 extensions maximum below Cand Eb). These chords cannot be repeated, so this section canpotentially be embellished for six bars with the current availabletextures.

D.7.1 Initial Observations of Section 2

1. In this section, as in the following section, the main texture ofsemiquavers [1] and [3] are based on the first two notes of the tonictriad: C and Eb. In this section, there is a 50% chance that the C willappear in the bass and the Eb will appear in the treble, and vice versa.

2. Semiquaver positions [4] no longer involve a neighbouring extensionfrom the bar's chord, but an alternative voicing of the chord used atposition [0] or [2]. If position [4] is copying the chord at position[2], this chord is inevitably the dominant of the featured chord in thefiguration: C minor global tonic. If position [4] is not copyingposition [2], then the 5th and 7th are used instead of the 3rd and 5thwhich appear at [2]. If the chord at position [4] is the one at position[0] then we select alternative notes from the first instance of thechord and randomise the direction of the arpeggio movement. Havingalternative notes can only happen for the two positions if there arefour notes in the given chord, such as the diminished in this case, orelse a note from a normal triad would have to be repeated by necessity.Although statistical information to support these assertions is limited,this interpretation gives a large generative potential.

3. This type of figuration is new, reversing the movement direction ofneighbouring notes at position [4] from the ones we have in theheuristics for Section 1. Rather than falling at position [2] as in thefirst set of algorithms for bars 1 to 18, the option exists to rise atposition [2] and then fall at position [4]. This offers a vast plethoraof generative possibilities compared to the first section's somewhatrigid pattern. This means that the system and its methodology iscreating algorithmic components which are generating original textureswithout any evidence of the textures ever having existed.

4. There is nothing stating that this section, based on these developedrules, could not be extended further to increase the length of thisbuild up. If the chord chosen for position [0] never repeats, thefiguration should never become a different cue from the overall build upin tension that this section is creating, and therefore it should beextendable. The full range of available chords are not equallyeffective, depending on whether they extend below the C and Eb by one,two or three extensions.

D.7.2 Heuristics for Section 2: Bars 19 to 20

D.7.2.1 H2.0: Calculate Bass at [1] This is initially 50% randomly thetonic below C3 or the 3rd of the tonic chord below C3. (This ignores anyvoice leading from the previous phrase in preference of an appropriaterange for the current voicings.)

D.7.2.2 H2.1: Calculate Bass at [2]

This heuristic extends H1.2:

If the bass at [1] is the 5th, then make this the 7th of the dominant7th (of the featured chord in the main figuration), below bass at [1].

If the bass at [1] is the 3rd, then make this the 5th of the dominant7th below bass at [1].

Adding to this:

If the bass at [1] is the 1st, then make this the 3rd of the dominant7th below bass at [1].

D.7.2.3 H2.2: Preparation for H2.3

This heuristic places a value in the bass at position [0] which iseither 1 or 2 (50%/50%) chord-component positions below the bass atposition [1]. This value will now randomise a given probability treebranch for H2.3.

D.7.2.4 H2.3: Calculate Bass at [4]

50% of the time this follows H1.3 (which requires the note generated byH2.2).

The other 50% we make [4] the next chord-component position of thedominant 7th above the dominant 7th's related note at [2].

D.7.2.5 H2.4: Calculate Treble at [1]

If the bass at [1] is the root of the prevailing chord, then make trebleat [1] 3rd plus an octave.

Else make treble at [1] the root, but in the octave that gives a pitchabove the bass at [1].

D.7.2.6 H2.5: Calculate Treble at [2]

Copy of H1.5.

D.7.2.7 H2.6: Calculate Treble at [4]

50% of the time we make this the next extension in the chord above thevalue in treble position [1].

The other 50% we make [4] the next chord-component position of thedominant 7th above the dominant 7th's related note at [2].

D.7.2.8 H2.7: Check Availability of Pitches for Notes from the ExtensionChord.

This heuristic checks the pitch range available for the notes inposition [0] in both the treble and bass, where we intend to place chordnotes from chords featured in the score of FIG. 32 . This process ishighlighted in the keyboard representation of FIG. 33 . Obtain aninteger range from a minor third below the treble's lowest note and aminor third above the bass's highest note.

Check that the desired second chord's 1st or 3rd appear in this range(the chord elements are referred to here as “1” and “2” respectively).

Obtain an integer range from a minor third below the bass's lowest noteand an octave below the bass's highest note.

If one note out of “1” and “2” is available in the middle range, thencheck the other is available in this range.

If both “1” and “2” are available in the middle range then check that atleast one of them is available in this range.

In the case of all notes being placeable, then distribute themappropriately in treble and bass positions [0]. (This will overwrite thetemporary value in bass [0].)

Else return to H2.0 and start again whilst keeping an array of thecreated values for all H2.x heuristics so far. Only store the values ifthey change.

This means that when we have four different versions of the output, ifH2.7 still has not been satisfied, we need to request an alteration tothe chord scheme and then we reset the storage array and start againfrom H2.0.

(The distribution logic should reflect the following:If one note out of “1” and “2” is available in the middle range thenplace it here and the other in the lower obtained range below the bass.If one note out of “1” and “2” is available in the bottom range thenplace it here and the other in the middle obtained range in between bassand treble.If both are available then randomly assign one to each range.)

D.7.2.9 H2.8: Copy the Bass and Treble to Fill Positions.

Copy of H1.8.

D.8 Section 3: Bars 21-24

Whereas Section 2 used C and Eb to extend chords downwards, this sectionuses the C and Eb texture as a basis for cadencing and extendingextensions upwards. The phrase analysis in Section C.5.7 is capable ofgenerating a chord scheme which provides the cadential, build up.

D.8.1 Initial Observations

1. This section contains a repeating texture in a similar way to the H2set. There is a higher chance that the treble and bass at position [4]will use the dominant 7th of the bar's chord to obtain their pitches.

2. The use of the diminished chord over the G pedal in bar 22 atposition [4] shows that the cadence chords generated by the phraseanalysis rules do not just have be the dominant. They can in fact be anychord that is conventionally one cadence position away from the tonic.We can discover candidate chords by gathering evidence from this piecein general, as well as other works of the time. The featured cadencechords here are an F sharp diminished seventh and a dominant b9. Thedominant 7th b9 features highly throughout the rest of the climax (whichis excluded from this analysis) from bar 25 to the end.

D.8.2 Heuristics for Section 3: Bars 21 to 24 D.8.2.1 H3.0: CalculateBass at [0]

This is the dominant above the initial bass tonic in bar 1, bassposition [1] of the piece. (This ignores the possibility of modulationfor the current study.)

D.8.2.2 H3.1: Calculate Bass at [1]

Extends H2.0. If this is the second bar of the section, simply copy thepitch calculated by this heuristic in the previous bar.

D.8.2.3 H3.2: Calculate Bass at [2]

Copy of H2.1

D.8.2.4 H3.3: Calculate Bass at [4]

Copy of H2.3

D.8.2.5 H3.4: Calculate Treble at [1] Extends H2.4. If this is thesecond bar of the section, simply copy the pitch calculated by thisheuristic in the previous bar.

D.8.2.6 H3.5: Calculate Treble at [2]

Copy of H1.5.

D.8.2.7 H3.6: Calculate Treble at [4]

Copy of H2.6

D.8.2.8 H3.7: Calculate Treble at [0]

This finds the pitch, in any octave, of the next available note from thebar's chord which is closest to the previous bar's pitch in thisposition. For the initial pitch of the first bar, take the pitchposition which is the next above the highest note in the treble texturefor the bar.

D.8.2.9 H3.8: Copy the Bass and Treble to fill positions.

Copy of H1.8.

D.9 Results

It is important to note that we are not advocating that Bach's choiceswere restricted to one note only. We are saying quite the opposite: thathe was faced with multiple choices, but we generalise the majority ofthem with this algorithmic analysis of what he chose. The validatedapproach, reflected in the analysis, relies on this diversity of choicesto give us the flexibility of generative composition based on theprinciples we have abstracted.

The previously unexplained Ab in bar 14 can easily be accounted for ifwe consider the latter heuristics for Sections 2 and 3. Randomlyintroducing these heuristics in place of earlier ones gives us theability to explain these notes. A set of aesthetic heuristics whichobserve and copy random choices from neighbouring bars, as well ashaving the ability to interchange heuristics from other sectionsrandomly, would produce the original score.

It is noticeable throughout latter sets of heuristics that previous onesare being reused and extended more and more frequently. This pointstowards an object-orientated approach for heuristic data representation.The extension of H1.2 for H2.1 shows that we should be able to overridemethods to add functionality, calling their super-type methods for anyprevious logic.

D.10 Conclusions

We have implemented a system of colouring entropic, redundant anddeveloped material which shows us when to generate heuristics as well asgiving us their functional purpose. Entropic (red/darker tone) markingsin the analysis require generative heuristics which create freshmaterial; redundant (green/mid-tone) markings require copy heuristics tofill out the generative material and developed (yellow-lightest tone)material shows the need for function heuristics which alter the outputof generative heuristics. We have three sets of heuristics which canaccount for all but two notes in the original piece as well as manyalternatives.

We have shown that Bach's earliest version of the prelude in theClavier-Buchlein manuscript agrees with the general heuristics derivedhere from the first section, removing the entropic thorns in the side ofthe opening section's analysis in bars 14 and 18. This shows that wehave created a set of rules which are closely compatible with Bach'soriginal compositional approach to this piece.

Unless specific arrangements are mutually exclusive with one another,the various embodiments described herein can be combined to enhancesystem functionality and/or to produce complementary functions or systemthat support the effective identification of user-perceivablesimilarities and dissimilarities. Such combinations will be readilyappreciated by the skilled addressee given the totality of the foregoingdescription. Likewise, aspects of the preferred embodiments may beimplemented in standalone arrangements where more limited functionalarrangements are appropriate. Indeed, it will be understood that unlessfeatures in the particular preferred embodiments are expresslyidentified as incompatible with one another or the surrounding contextimplies that they are mutually exclusive and not readily combinable in acomplementary and/or supportive sense, the totality of this disclosurecontemplates and envisions that specific features of those complementaryembodiments can be selectively combined to provide one or morecomprehensive, but slightly different, technical solutions. In terms ofthe suggested process flows of the accompanying drawings, it may be thatthese can be varied in terms of the precise points of execution forsteps within the process so long as the overall effect or re-orderingachieves the same objective end results or important intermediateresults that allow advancement to the next logical step. The flowprocesses are therefore logical in nature rather than absolute. Thefunctional architectures of the drawings may be implementedindependently of one another, as will be understood, so that theresulting system is a distributed system potentially dispersed via awide area network, such as the Internet. Architecturally, realization ofaspects of the system, such as but not limited to texture classificationas described herein (as a basis for final automated musical composition)can be implemented using technologies such as the Java Expert SystemShell “JESS” and, more typically, a bespoke expert system.

Aspects of the present invention may be provided in a downloadable formor otherwise on a computer readable medium, such as a CD ROM, thatcontains program code that, when instantiated, executes the linkembedding functionality at a web-server or the like.

The doctoral thesis of Joseph Michael William Lyske titled “MetaCreation for Film Scores”, contemporaneously and first published on 31Mar. 2021 by the School of Electronic Engineering and Computer Science,Queen Mary, University of London, is incorporated in its entirety hereinby reference.

The invention disclosed herein is applicable to any musical scale andany cultural precondition, not just Western music which has been used asan exemplary format.

As disclosed herein, whilst the Form Atom provides an extremelyimportant building block upon which generative composition can be based,the totality of the disclosure includes multiple independent (butrelated) aspects that, together, provide a comprehensive implementationhaving considerable detail, including the use of the hypernodeframework. For example, from a composition perspective, theclassification and manipulation of textures is highly significant. Forexample, stand-alone technical solutions are related to the process bywhich chord spacing is determined, as well as how primitives aredeveloped and employed within the context of building a generativesystem.

It will, of course, be appreciated that the above description has beengiven by way of example only and that modifications in detail may bemade within the scope of the present invention. For example, whilst thegenerative system has been expressed in the context of Western musichaving a particular degree of scale, the techniques are commutable toother styles and metres.

The analysis technique, coupled with the generative framework, gives afoundation for looking at music hierarchically in a way that leads toeffective output. This is not only a useful method of creatingaesthetically functional generative film composition and game scoresthat can, in fact, be orchestrated personally by the user provided thatthey are given access to the system via an interface and a databasecontaining Form Atoms meta-tagged to artists and songs of their personalliking.

Completely autonomous solutions are feasible, based on the givenhierarchy, in which computers analyse works and compose music based onanalysis. For example, a trained artificial intelligence mechanism, suchas deep learning neural networks and generative algorithms withassociated fitness functions, can learn how to select appropriateprimitives based on a score. This approach leads to more efficient waysto create ever smaller sets of heuristics [Occam's Razor] that cangenerate the same standard of output from the same set of analysedcompositions. The only thing then left for humans potentially to dowould be to meta-tag the emotional concepts, although even this task canbe made the subject of AI networks (such as those in described in US2020-0320398 and related works) that close the semantic gap and whichmake use of NLP or file properties to correlate to with emotionalperception. The skilled person will thus understand which aspects of thesystem intelligence may benefit for different forms of processor.

1-22. (canceled)
 23. A computer-implemented method of generating amusical composition in which the generative composition contains aplurality of musical texture groups, the method comprising: i)assembling musical texture groups from musical instrument components,wherein: a) each of said musical texture groups has an associated tagexpressing emotional textural connotation b) each musical instrumentcomponent has musical textural classifiers selected from a set ofpre-defined musical textural classifiers and such that: i) differentmusical instrument components may include a differing subset ofpre-defined musical textural classifiers; and ii) each musicalinstrument component has either a musical accompaniment attribute or amusical feature attribute, and iii) where each musical texturalclassifier that is present within a musical texture group possesses: aa)either no musical feature attribute or a single musical featureattribute, and bb) any number of musical accompaniment attributes,including no musical accompaniment attribute, and c) different musicaltexture groups can have a tag having a common emotional texturalconnotation or a similar emotional textural connotation having anassociation with the common emotional textural connotation tag, but atthe same time different musical texture groups have differing subsets ofmusical textural classifiers or differing musical attributes for eachmusical textural component; ii) generating at least one chord scheme toa narrative brief, wherein the chord scheme is based on selecting andassembling Form Atoms and the briefing narrative provides an emotionalconnotation to a series of events; and iii) applying a texture to the atleast one chord scheme to generate the musical composition reflectingthe briefing narrative; and where each Form Atoms has self-containedconstructional properties representative of an historical corpus ofmusic and each Form Atom has: a generative set of heuristics thatsupports generation of a set of chords in a chord scheme or manydifferent sets of chords in the same or different tonics that achievethe same form function and which thus have similar associatedemotional/musical connotations, and chord spacer heuristics that spaceout temporally any number of generated chords for any given length ofmusical time; a tag that describes compositional heuristics of itsrespective Form Atom; a chord list in a local tonic where the chord listdefines branching structures giving options for generation of differentchords from the local tonic, and a progression descriptor in combinationwith a form function that expresses musically one of a question, ananswer and a statement, and wherein each Form Atoms creates a meta-mapof a chord scheme in a musical section; and wherein musical transitionsbetween Form Atoms are mapped to identify and then record establishedtransitions between Form Atoms in multiple original scores and suchthat, within the system, groups exist in which Form Atoms are identifiedas having similar tags but different constructional properties and tagsof selected Form Atoms are related to the emotional textural connotationtag of related musical texture groups.
 24. The computer-implementedmethod of claim 23, wherein the musical textural classifiers areselected from a group comprising at least some of melody,counter-melody, harmony, bass, pitched rhythm, non-pitched rhythm anddrums.
 25. The computer-implemented method of claim 23, wherein amusical feature is: a salient musical component in musical texture; andcontains information about musical tension and release within themusical section and which tension and release would be musicallycontextually destroyed if the musical feature were to be combined withanother musical feature in the musical section and in the samepre-defined musical textual classifier.
 26. The computer-implementedmethod of claim 23, wherein an accompaniment does not interfere withanother accompaniment or a feature in any specific textual classifier ofa musical section and can be added or removed selectively to thicken orthin the texture of the musical section.
 27. The computer-implementedmethod of claim 23, wherein the musical instrument components contain:pitch data in the form of core heuristics, and rhythm data in the formof drum heuristics within a kit.
 28. The computer-implemented method ofclaim 27, further comprising: aggregating desired kits; applyinginternal storage and external MIDI mapping to cause physical output thegenerative composition.
 29. The method of claim 23, further comprising:identifying absence of a textural narrative in a first musical sectionconcatenated with a second music section having a texture profile; andfiling the first musical section with at least one component that is amusical accompaniment or a musical feature selection of the at least onecomponent is based on one of: history of preceding textural classifiersand a continuation of a dominant one of the textural classifiers, else alogical bridge between a destination subset of pre-defined musicaltextural classifiers based on intensity of respective subsets.